diff --git a/properties/P000010.md b/properties/P000010.md
index 107e2e461..fcaa52149 100644
--- a/properties/P000010.md
+++ b/properties/P000010.md
@@ -14,6 +14,7 @@ Defined in 14E of {{zb:1052.54001}}.
 ----
 ### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to open sets.
 - This property is not hereditary with respect to closed sets
 (Example: {S11|P10}
diff --git a/properties/P000014.md b/properties/P000014.md
index f66624924..0bfccfc79 100644
--- a/properties/P000014.md
+++ b/properties/P000014.md
@@ -22,4 +22,5 @@ Defined on page 11 of {{zb:0386.54001}} (as $T_5$).
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
diff --git a/properties/P000015.md b/properties/P000015.md
index bf02a3474..2954009c0 100644
--- a/properties/P000015.md
+++ b/properties/P000015.md
@@ -31,4 +31,5 @@ Defined on page 16 of {{zb:0386.54001}} (as perfectly $T_4$).
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary (see Theorem 2.1.6 in {{zb:0684.54001}}).
diff --git a/properties/P000017.md b/properties/P000017.md
index 2090a6a40..f1e74dbfd 100644
--- a/properties/P000017.md
+++ b/properties/P000017.md
@@ -9,3 +9,8 @@ refs:
 A space which is the union of countably many {P16} subsets.
 
 Defined on page 19 of {{zb:0386.54001}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000019.md b/properties/P000019.md
index a3d394322..723823a4b 100644
--- a/properties/P000019.md
+++ b/properties/P000019.md
@@ -19,4 +19,5 @@ Defined on page 19 of {{zb:0386.54001}}.  See for example {{wikipedia:Countably_
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to closed sets.
diff --git a/properties/P000020.md b/properties/P000020.md
index c79731939..1f5e85fcf 100644
--- a/properties/P000020.md
+++ b/properties/P000020.md
@@ -15,5 +15,6 @@ Defined on page 19 of {{zb:0386.54001}}.
 ---
 ### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to closed sets.
 - This property is preserved by countable products (see Theorem 3.10.35 in {{zb:0684.54001}}).
diff --git a/properties/P000022.md b/properties/P000022.md
index 303afb6bc..7c418c64b 100644
--- a/properties/P000022.md
+++ b/properties/P000022.md
@@ -13,4 +13,5 @@ Defined on page 20 of {{zb:0386.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is preserved in any coarser topology.
diff --git a/properties/P000024.md b/properties/P000024.md
index 6fe677d55..23941161b 100644
--- a/properties/P000024.md
+++ b/properties/P000024.md
@@ -16,3 +16,8 @@ Equivalently (see Condition 2 of {{wikipedia:Locally_compact_space}}), every poi
 a closed and compact neighborhood.
 
 Defined on page 20 of {{zb:0386.54001}} as "strongly locally compact". Contrast with {P130}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000025.md b/properties/P000025.md
index c015825a7..be7443a4f 100644
--- a/properties/P000025.md
+++ b/properties/P000025.md
@@ -22,3 +22,8 @@ Equivalently, $X=\bigcup_{n<\omega}K_n$ for $K_n$ compact, and such that $K_n\su
 The equivalences above can be shown using the ideas in {{mathse:4568032}}.
 
 Defined on page 21 of {{zb:0386.54001}} as "$\sigma$-locally compact".
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000027.md b/properties/P000027.md
index 3a6186055..092c69157 100644
--- a/properties/P000027.md
+++ b/properties/P000027.md
@@ -13,4 +13,5 @@ Defined on page 7 of {{zb:0386.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
diff --git a/properties/P000029.md b/properties/P000029.md
index 5f993758d..e79d136fb 100644
--- a/properties/P000029.md
+++ b/properties/P000029.md
@@ -17,3 +17,8 @@ A space in which every collection of pairwise-disjoint nonempty open sets is cou
 
 Defined on page 22 of {{zb:0386.54001}}.
 Also referred to as the "Suslin/Souslin property" as in e.g. 1.7.12 of {{zb:0684.54001}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000031.md b/properties/P000031.md
index 1cdd14c7e..05b493168 100644
--- a/properties/P000031.md
+++ b/properties/P000031.md
@@ -18,4 +18,5 @@ Defined on page 23 of {{zb:0386.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to closed sets.
diff --git a/properties/P000032.md b/properties/P000032.md
index 7a7477b95..3b2c02f17 100644
--- a/properties/P000032.md
+++ b/properties/P000032.md
@@ -13,4 +13,5 @@ Defined on page 23 of {{zb:0386.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to closed sets.
diff --git a/properties/P000034.md b/properties/P000034.md
index 4188b0b13..40eecfeae 100644
--- a/properties/P000034.md
+++ b/properties/P000034.md
@@ -35,3 +35,8 @@ Also see [Henno Brandsma: On paracompactness, full normality and the like](http:
 
 (Note: {{zb:0386.54001}} defines this property on page 23 as "fully $T_4$".
 Misleadingly, it also calls "star refinement" what all other major sources call a barycentric refinement.)
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000039.md b/properties/P000039.md
index 911859c10..1fa14fba3 100644
--- a/properties/P000039.md
+++ b/properties/P000039.md
@@ -24,6 +24,7 @@ See {{wikipedia:Hyperconnected_space}} for other equivalent characterizations.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to open sets.
 - This property is preserved by arbitrary products.
 - This property is preserved by continuous images.
diff --git a/properties/P000040.md b/properties/P000040.md
index 4e791c20c..785b8d28f 100644
--- a/properties/P000040.md
+++ b/properties/P000040.md
@@ -14,3 +14,8 @@ Equivalently ({{mathse:5006424}}), the only neighborhood of the space's
 diagonal $\Delta=\{\langle x,x\rangle:x\in X\}$ is $X^2$.
 
 Defined on page 29 of {{zb:0386.54001}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000041.md b/properties/P000041.md
index b12492849..ce573ce0f 100644
--- a/properties/P000041.md
+++ b/properties/P000041.md
@@ -32,4 +32,5 @@ Defined on page 30 of {{zb:0386.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to open sets.
diff --git a/properties/P000042.md b/properties/P000042.md
index bf3f70a21..e89c78675 100644
--- a/properties/P000042.md
+++ b/properties/P000042.md
@@ -44,4 +44,5 @@ Compare with {P43} and {P96}.
 ----
 ### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to open sets.
diff --git a/properties/P000049.md b/properties/P000049.md
index a54e17224..47bad7b96 100644
--- a/properties/P000049.md
+++ b/properties/P000049.md
@@ -26,6 +26,7 @@ which we do not assume here.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to open sets (see Problem 15G.2 in {{zb:1052.54001}}).
 - This property is hereditary with respect to dense sets (see {{mathse:3769214}}).
 - This property is hereditary with respect to locally dense sets (equivalent to previous two meta-properties; see also Proposition 1 of {{mathse:5025114}}).
diff --git a/properties/P000050.md b/properties/P000050.md
index 3cf4bcc19..6e277e63f 100644
--- a/properties/P000050.md
+++ b/properties/P000050.md
@@ -13,5 +13,6 @@ Defined on page 33 of {{zb:0386.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
 - This property is preserved by arbitrary products.
diff --git a/properties/P000054.md b/properties/P000054.md
index 22b0ca48f..b43e85511 100644
--- a/properties/P000054.md
+++ b/properties/P000054.md
@@ -15,5 +15,6 @@ Defined on page 37 of {{zb:0386.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
 - This property is preserved by arbitrary disjoint unions.
diff --git a/properties/P000056.md b/properties/P000056.md
index e0c39b725..a959abb64 100644
--- a/properties/P000056.md
+++ b/properties/P000056.md
@@ -17,4 +17,5 @@ Defined on page 7 of {{zb:0386.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is preserved by arbitrary disjoint unions.
diff --git a/properties/P000060.md b/properties/P000060.md
index a2b4f1f94..60578501d 100644
--- a/properties/P000060.md
+++ b/properties/P000060.md
@@ -13,3 +13,8 @@ refs:
 Every continuous function $f:X \to \mathbb R$ is constant.
 
 Defined on page 223 of {{zb:0386.54001}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000062.md b/properties/P000062.md
index 687421c5b..bb5ed2658 100644
--- a/properties/P000062.md
+++ b/properties/P000062.md
@@ -11,6 +11,7 @@ Every open cover of $X$ has a countable subcollection whose union is dense in $X
 ----
 ### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to clopen sets.
 - This property is preserved in any coarser topology.
 - If a nonempty product space satisfies the property, so does every factor.
diff --git a/properties/P000064.md b/properties/P000064.md
index 55a34015a..de0dc76ce 100644
--- a/properties/P000064.md
+++ b/properties/P000064.md
@@ -11,3 +11,8 @@ refs:
 A space such that the countable union of closed nowhere dense subsets has empty interior; equivalently, such that the countable intersection of open dense subsets is still dense.
 
 See {{wikipedia:Baire_space}} for several other equivalent characterizations.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000066.md b/properties/P000066.md
index f85d95902..b9fb4b578 100644
--- a/properties/P000066.md
+++ b/properties/P000066.md
@@ -16,4 +16,5 @@ See section 5 of {{doi:10.1016/0166-8641(95)00067-4}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to closed sets.
diff --git a/properties/P000068.md b/properties/P000068.md
index eb094a9b9..ee668aced 100644
--- a/properties/P000068.md
+++ b/properties/P000068.md
@@ -17,4 +17,5 @@ See section 6 of {{doi:10.1016/0166-8641(95)00067-4}}.
 
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to closed subspaces.
diff --git a/properties/P000069.md b/properties/P000069.md
index 263d3483a..706a0fffc 100644
--- a/properties/P000069.md
+++ b/properties/P000069.md
@@ -20,4 +20,9 @@ Strategic Menger: The second player has a winning strategy in the Menger game. S
 
 Strategically $\Omega$-Menger: The second player has a winning strategy in the game $\mathsf{G}_{\mathrm{fin}}(\Omega_X,\Omega_X)$. See pages 2 and 3 of {{doi:10.1016/j.topol.2019.07.008}} for more details.
 
-The equivalence of Strategic Menger and Strategically $\Omega$-Menger is Theorem 35 of {{doi:10.1016/j.topol.2019.02.062}}.
\ No newline at end of file
+The equivalence of Strategic Menger and Strategically $\Omega$-Menger is Theorem 35 of {{doi:10.1016/j.topol.2019.02.062}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000070.md b/properties/P000070.md
index 5dfa65b3f..3e1331eb0 100644
--- a/properties/P000070.md
+++ b/properties/P000070.md
@@ -17,4 +17,9 @@ Markov Menger: The second player has a Markov winning strategy in the Menger gam
 
 Markov $\Omega$-Menger: The second player has a Markov winning strategy in the game $\mathsf{G}_{\mathrm{fin}}(\Omega_X,\Omega_X)$ (relying on only the round number and most recent move of the opponent). See pages 2 and 3 of {{doi:10.1016/j.topol.2019.07.008}} for more details.
 
-The equivalence of Markov Menger with Markov $\Omega$-Menger is established in {{mathse:4730419}}.
\ No newline at end of file
+The equivalence of Markov Menger with Markov $\Omega$-Menger is established in {{mathse:4730419}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000079.md b/properties/P000079.md
index 78805c7a6..5832281ac 100644
--- a/properties/P000079.md
+++ b/properties/P000079.md
@@ -17,6 +17,7 @@ Equivalently, for every set $A\subseteq X$ that is *not* closed in $X$, there is
 ----
 ### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to closed sets (see {{mathse:479808}}).
 - This property is hereditary with respect to open sets (see {{mathse:479808}}).
 - This property is preserved by quotient maps.
diff --git a/properties/P000080.md b/properties/P000080.md
index bf16ed491..ad1491bed 100644
--- a/properties/P000080.md
+++ b/properties/P000080.md
@@ -17,5 +17,6 @@ Compare with {P172}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
 
diff --git a/properties/P000090.md b/properties/P000090.md
index 511f5d1a6..749013849 100644
--- a/properties/P000090.md
+++ b/properties/P000090.md
@@ -27,6 +27,7 @@ See also {{zb:0944.54018}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
 - This property is preserved by arbitrary disjoint unions.
 - This property is preserved by finite products.
diff --git a/properties/P000098.md b/properties/P000098.md
index 714bb4bbe..e411a4505 100644
--- a/properties/P000098.md
+++ b/properties/P000098.md
@@ -22,3 +22,8 @@ its intersection with each $K_n$ is closed (resp. open) in $K_n$.
 Defined as "$k_\omega$-space" on page 13 of {{zb:0288.22006}}.
 The corresponding notion requiring that each $K_n$ be {P3} is {P92}.
 See also {P140}, {P141}, and {P142}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000105.md b/properties/P000105.md
index 1a873b5a8..9c63e5230 100644
--- a/properties/P000105.md
+++ b/properties/P000105.md
@@ -13,4 +13,5 @@ Defined on page 200 of {{zb:1059.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is preserved by arbitrary disjoint unions.
diff --git a/properties/P000108.md b/properties/P000108.md
index 939256fee..d644ab9dd 100644
--- a/properties/P000108.md
+++ b/properties/P000108.md
@@ -24,5 +24,6 @@ For the equivalence of the conditions above, see {{mathse:4737011}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
 - This property is preserved by arbitrary disjoint unions.
diff --git a/properties/P000117.md b/properties/P000117.md
index fd821f6ba..7615ddf81 100644
--- a/properties/P000117.md
+++ b/properties/P000117.md
@@ -15,4 +15,5 @@ See for example page 127 of {{zb:0684.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
diff --git a/properties/P000128.md b/properties/P000128.md
index 5b5098e5b..727eac7b7 100644
--- a/properties/P000128.md
+++ b/properties/P000128.md
@@ -8,4 +8,9 @@ refs:
 
 Every open $k$-cover of $X$ has a countable $k$-subcover.  (A family $\mathcal U$ of open subsets of $X$ is called a *$k$-cover* if each compact subset of $X$ is contained in an element of $\mathcal U$ and $X \notin \mathcal U$.)
 
-Defined on page 3279 of {{doi:10.1016/j.topol.2005.07.015}}.
\ No newline at end of file
+Defined on page 3279 of {{doi:10.1016/j.topol.2005.07.015}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000129.md b/properties/P000129.md
index ef146e331..229b28b87 100644
--- a/properties/P000129.md
+++ b/properties/P000129.md
@@ -15,4 +15,5 @@ See 3.2d of {{zb:1052.54001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
diff --git a/properties/P000130.md b/properties/P000130.md
index 76d661a49..1ebec9041 100644
--- a/properties/P000130.md
+++ b/properties/P000130.md
@@ -12,6 +12,7 @@ Given as condition (3) in {{wikipedia:Locally_compact_space}}.  See also the art
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to open sets.
 - This property is hereditary with respect to closed sets.
 - This property is hereditary with respect to locally closed sets (equivalent to previous two meta-properties).
diff --git a/properties/P000140.md b/properties/P000140.md
index 4d1f06a79..248f975a6 100644
--- a/properties/P000140.md
+++ b/properties/P000140.md
@@ -22,6 +22,7 @@ Equivalently, a space whose topology coincides with the final topology with resp
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to closed sets.
 - This property is not hereditary with respect to open sets
 (e.g., {S23}, open in {S165}).
diff --git a/properties/P000146.md b/properties/P000146.md
index 0fcfa31fa..65ddd70ae 100644
--- a/properties/P000146.md
+++ b/properties/P000146.md
@@ -21,4 +21,5 @@ The equivalence between the two definitions is shown in Lemma 1.3 and Corollary
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is preserved by arbitrary disjoint unions.
diff --git a/properties/P000149.md b/properties/P000149.md
index e499d9e3e..1967181ca 100644
--- a/properties/P000149.md
+++ b/properties/P000149.md
@@ -26,4 +26,5 @@ as the fifth item "$\varepsilon$" in a list from
 ---
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to closed sets.
diff --git a/properties/P000150.md b/properties/P000150.md
index 8873b3b19..cba401aa3 100644
--- a/properties/P000150.md
+++ b/properties/P000150.md
@@ -12,3 +12,8 @@ The space satisfies the selection principle $\mathsf S_1(\Omega,\Omega)$: for ev
 Equivalently, every finite power of $X$ is {P68}.
 
 See {{doi:10.1090/S0002-9939-1988-0964873-0}}; the equivalence with every finite power being {P68} is on page 918.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000152.md b/properties/P000152.md
index b9a60b70b..3a8f0987b 100644
--- a/properties/P000152.md
+++ b/properties/P000152.md
@@ -21,3 +21,8 @@ Equivalent conditions:
 - Topologically countable: There is a set $\{ x_n : n \in \omega \} \subseteq X$ so that, for every $x \in X$, there is some $n \in \omega$ so that every neighborhood of $x_n$ contains $x$. See {{zb:1555.54009}} for more on this property.
 
 The equivalence is shown in Theorem 4.17 of {{zb:1555.54009}} and also at {{mathse:4737285}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000153.md b/properties/P000153.md
index d74ff7400..de70aa09d 100644
--- a/properties/P000153.md
+++ b/properties/P000153.md
@@ -12,3 +12,8 @@ The space satisfies the selection principle $\mathsf S_{\mathrm{fin}}(\Omega,\Om
 Equivalently, every finite power of $X$ is {P66}.
 
 See {{doi:10.1016/S0166-8641(96)00075-2}}; the equivalence with every finite power being {P66} is Theorem 3.9.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000156.md b/properties/P000156.md
index ff32ee0d0..5c6f80bc2 100644
--- a/properties/P000156.md
+++ b/properties/P000156.md
@@ -8,3 +8,8 @@ refs:
 
 The space satisfies the selection principle $\mathsf S_1(\mathcal K,\mathcal K)$: for every sequence $\langle \mathscr U_n : n \in \omega \rangle$ of $k$-covers of $X$, there exist choices $U_n \in \mathscr U_n$ so that $\{ U_n :n \in \omega \}$ is a $k$-cover of $X$.
 (A family $\mathcal U$ of open subsets of $X$ is called a *$k$-cover* if each compact subset of $X$ is contained in an element of $\mathcal U$ and $X \notin \mathcal U$.)
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000157.md b/properties/P000157.md
index 5dc388c25..ff4ace989 100644
--- a/properties/P000157.md
+++ b/properties/P000157.md
@@ -6,3 +6,8 @@ refs:
   name: Selection games and the Vietoris space
 ---
 The second player has a winning strategy in the game $\mathsf{G}_1(\mathcal K_X,\mathcal K_X)$. See Remark 2.4 and Definition 2.7 of {{doi:10.1016/j.topol.2021.107772}} for more details.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000159.md b/properties/P000159.md
index d7d2b64a4..737164734 100644
--- a/properties/P000159.md
+++ b/properties/P000159.md
@@ -8,3 +8,8 @@ refs:
 
 The space satisfies the selection principle $\mathsf S_{\mathrm{fin}}(\mathcal K,\mathcal K)$: for every sequence $\langle \mathscr U_n : n \in \omega \rangle$ of $k$-covers of $X$, there exist choices $\mathcal F_n$, a finite subset of $\mathscr U_n$, so that $\bigcup_{n\in\omega} \mathcal F_n$ is a $k$-cover of $X$.
 (A family $\mathcal U$ of open subsets of $X$ is called a *$k$-cover* if each compact subset of $X$ is contained in an element of $\mathcal U$ and $X \notin \mathcal U$.)
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000160.md b/properties/P000160.md
index f9cf36028..ea45c6f35 100644
--- a/properties/P000160.md
+++ b/properties/P000160.md
@@ -6,3 +6,8 @@ refs:
   name: Selection games and the Vietoris space
 ---
 The second player has a winning strategy in the game $\mathsf{G}_{\mathrm{fin}}(\mathcal K_X,\mathcal K_X)$. See Remark 2.4 and Definition 2.7 of {{doi:10.1016/j.topol.2021.107772}} for more details.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000161.md b/properties/P000161.md
index 96f2b057a..ff97a8eab 100644
--- a/properties/P000161.md
+++ b/properties/P000161.md
@@ -5,4 +5,9 @@ refs:
 - doi: 10.1016/j.topol.2021.107772
   name: Selection games and the Vietoris space
 ---
-The second player has a Markov winning strategy in the game $\mathsf{G}_{\mathrm{fin}}(\mathcal K_X,\mathcal K_X)$ (relying on only the round number and most recent move of the opponent). See Remark 2.4 and Definition 2.7 of {{doi:10.1016/j.topol.2021.107772}} for more details.
\ No newline at end of file
+The second player has a Markov winning strategy in the game $\mathsf{G}_{\mathrm{fin}}(\mathcal K_X,\mathcal K_X)$ (relying on only the round number and most recent move of the opponent). See Remark 2.4 and Definition 2.7 of {{doi:10.1016/j.topol.2021.107772}} for more details.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000173.md b/properties/P000173.md
index 874075ed1..cea448340 100644
--- a/properties/P000173.md
+++ b/properties/P000173.md
@@ -11,3 +11,8 @@ refs:
 A space in which every radially closed set is closed, where a set $A\subseteq X$ is *radially closed* if it contains the limits of all convergent transfinite sequences consisting of points of $A$.  In other words, for every non-closed set $A\subseteq X$ there is a point $p\in \overline A\setminus A$ and a transfinite sequence $(x_\alpha)_{\alpha<\lambda}$ of points of $A$ that converges to $p$.  (Here $\lambda$ is a limit ordinal and can always be taken to be a regular cardinal.)
 
 See the chapter "d-4 Pseudoradial spaces" in {{zb:1059.54001}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000180.md b/properties/P000180.md
index 19e5cf03a..6c9f115e7 100644
--- a/properties/P000180.md
+++ b/properties/P000180.md
@@ -13,4 +13,5 @@ Defined on page 182 of {{doi:10.1016/B978-0-444-50355-8.X5000-4}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
diff --git a/properties/P000182.md b/properties/P000182.md
index ca1c62398..f4542652e 100644
--- a/properties/P000182.md
+++ b/properties/P000182.md
@@ -15,5 +15,6 @@ Defined on page 127 of {{zb:0684.54001}}.
 ---
 ### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
 - This property is preserved by countable products.
diff --git a/properties/P000183.md b/properties/P000183.md
index e5af30221..ba1ab5b08 100644
--- a/properties/P000183.md
+++ b/properties/P000183.md
@@ -32,6 +32,7 @@ See {{mr:206907}}, available at <https://www.jstor.org/stable/24901448>.
 ---
 ### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
 - This property is preserved by countable products (see Corollary in {{mo:506308}}).
 
diff --git a/properties/P000187.md b/properties/P000187.md
index ee74d7606..05dd0bb7b 100644
--- a/properties/P000187.md
+++ b/properties/P000187.md
@@ -20,6 +20,7 @@ See also section 2 of {{zb:1141.54020}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
 - This property is preserved by countable products (see Theorem 4.1 of {{zb:0327.54019}}).
 - This property is preserved by $\Sigma$-products (see Theorem 4.6 of {{zb:0327.54019}}).
diff --git a/properties/P000193.md b/properties/P000193.md
index e46fa9876..ab2f66ab6 100644
--- a/properties/P000193.md
+++ b/properties/P000193.md
@@ -15,3 +15,8 @@ refs:
 A space in which every open cover admits a shrinking; that is, a space $X$ in which, given any open cover $\{ U_\alpha : \alpha \in A\}$, there is an open cover $\{ V_\alpha : \alpha \in A\}$ such that $\overline{V_\alpha} \subseteq U_\alpha$ for each $\alpha \in A$.
 
 See also [Dan Ma's Topology Blog post on Spaces with shrinking properties](https://dantopology.wordpress.com/2017/01/05/spaces-with-shrinking-properties/).
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000194.md b/properties/P000194.md
index b0a9fd4db..2053e9c3c 100644
--- a/properties/P000194.md
+++ b/properties/P000194.md
@@ -18,4 +18,6 @@ This property was introduced in {{zb:0132.18401}} under the name of *$\theta$-re
 
 ---
 #### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary with respect to closed sets.
\ No newline at end of file
diff --git a/properties/P000196.md b/properties/P000196.md
index 42c201217..fefc1a9db 100644
--- a/properties/P000196.md
+++ b/properties/P000196.md
@@ -22,5 +22,6 @@ For proof of the equivalences and further characterizations, see section 12 of {
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
 - This property is preserved in any coarser topology.
diff --git a/properties/P000199.md b/properties/P000199.md
index a392d2e4a..4a3dddf23 100644
--- a/properties/P000199.md
+++ b/properties/P000199.md
@@ -21,4 +21,5 @@ Defined on page 4 of {{zb:1044.55001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is preserved by arbitrary products. (see {{mathse:4463999}})
diff --git a/properties/P000201.md b/properties/P000201.md
index aa084e7d6..67f08bc6a 100644
--- a/properties/P000201.md
+++ b/properties/P000201.md
@@ -27,4 +27,5 @@ See Definition 1.1.7 on page 3 of {{zb:1325.14001}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is preserved in any coarser topology.
diff --git a/properties/P000202.md b/properties/P000202.md
index 8669c4f8c..beae9edc1 100644
--- a/properties/P000202.md
+++ b/properties/P000202.md
@@ -26,4 +26,5 @@ Compare with {P201} and {P203}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is preserved in any coarser topology.
diff --git a/properties/P000207.md b/properties/P000207.md
index ab944d46f..6be673c12 100644
--- a/properties/P000207.md
+++ b/properties/P000207.md
@@ -30,5 +30,6 @@ See also {{doi:10.1090/S0002-9939-1981-0630058-4}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is preserved by arbitrary disjoint unions.
 - This property is hereditary with respect to closed sets (corollary of Theorem 4.1 in {{zb:0078.14803}}).
diff --git a/properties/P000208.md b/properties/P000208.md
index cf8152070..af44951e3 100644
--- a/properties/P000208.md
+++ b/properties/P000208.md
@@ -30,6 +30,7 @@ Compare with {P226}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
 - This property is preserved by finite products (see Theorem 3 in {{mathse:5118758}}).
 - This property is preserved by finite disjoint unions.
diff --git a/properties/P000209.md b/properties/P000209.md
index 330eaabb7..7be537df6 100644
--- a/properties/P000209.md
+++ b/properties/P000209.md
@@ -7,4 +7,6 @@ There exists a dense subset with cardinality $\leq \mathfrak c=2^{\aleph_0}=|\ma
 
 ----
 #### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is preserved by countable products.
diff --git a/properties/P000210.md b/properties/P000210.md
index 7ae5540a4..dc4fcb635 100644
--- a/properties/P000210.md
+++ b/properties/P000210.md
@@ -34,4 +34,5 @@ are due to Arkhangel'skii ({{zb:0275.54004}}).
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
diff --git a/properties/P000211.md b/properties/P000211.md
index 45bdf6518..5b8995354 100644
--- a/properties/P000211.md
+++ b/properties/P000211.md
@@ -33,4 +33,5 @@ This property was introduced by Nyikos in {{zb:0774.54019}}.
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
diff --git a/properties/P000212.md b/properties/P000212.md
index 0489e2f72..d403d3f14 100644
--- a/properties/P000212.md
+++ b/properties/P000212.md
@@ -33,4 +33,5 @@ are due to Arkhangel'skii ({{zb:0275.54004}}).
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
diff --git a/properties/P000213.md b/properties/P000213.md
index 8e5da280e..fe2687086 100644
--- a/properties/P000213.md
+++ b/properties/P000213.md
@@ -33,4 +33,5 @@ are due to Arkhangel'skii ({{zb:0275.54004}}).
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
diff --git a/properties/P000214.md b/properties/P000214.md
index 47a4b1e41..4d6db6015 100644
--- a/properties/P000214.md
+++ b/properties/P000214.md
@@ -33,4 +33,5 @@ are due to Arkhangel'skii ({{zb:0275.54004}}).
 ----
 #### Meta-properties
 
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is hereditary.
diff --git a/properties/P000218.md b/properties/P000218.md
index 7e2e9ce91..df415feda 100644
--- a/properties/P000218.md
+++ b/properties/P000218.md
@@ -25,3 +25,8 @@ See also page 1 of {{doi:10.48550/arXiv.1306.6086}}.
 
 The book {{zb:1471.54001}} uses "strongly zero-dimensional"
 for a space that is {P218} and non-empty (see page 9); {P218} is equivalent to either one of $\dim(X), \text{Ind}(X)$ or $\text{Ind}_0(X)$ being $\leq 0$. See chapters 2 and 13 for definitions of $\dim, \text{Ind}, \text{Ind}_0$.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000230.md b/properties/P000230.md
index 8ae7772be..daf920a08 100644
--- a/properties/P000230.md
+++ b/properties/P000230.md
@@ -17,3 +17,8 @@ Equivalently, for each $x \in X$, every neighborhood of $x$ contains a simply co
 Defined on page 298 of {{zb:1209.57001}}, and listed as property $P_1$ in {{mo:487326}}.
 
 Has also been called "strongly locally simply connected", for example in {{zb:0209.54802}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000231.md b/properties/P000231.md
index b43feef84..97dc1222f 100644
--- a/properties/P000231.md
+++ b/properties/P000231.md
@@ -11,3 +11,8 @@ refs:
 Every point of $X$ has a neighborhood which is {P200}. 
 
 Defined as "locally simply connected" on page 54 of {{zb:0063.00842}} and listed as property $P_4$ in {{mo:487326}}.
+
+----
+#### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
diff --git a/properties/P000232.md b/properties/P000232.md
index 7e24ecbcb..99fa6c145 100644
--- a/properties/P000232.md
+++ b/properties/P000232.md
@@ -36,4 +36,6 @@ Listed as property $P_{10}$ in {{mo:487326}}.
 
 ----
 #### Meta-properties
+
+- $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does.
 - This property is preserved by retractions (use Theorem 16.2 on p. 29 of {{zb:0153.52905}}).