Adjustments

Author: GeoffreySangston

properties/P000225.md

@@ -12,7 +12,7 @@ refs:
     name: Encyclopedia of general topology
 ---
 
-$X$ is $LC$ if every neighborhood $U$ of any point $x$ contains a neighborhood $V$ of $x$ that is contractible in $U$. 
+Every neighborhood $U$ of any point $x$ contains a neighborhood of $x$ that is contractible in $U$. 
 
 Equivalently, $X$ is locally contractible at each of its points. A space $X$ is *locally contractible at a point* $x \in X$ if every neighborhood $U$ of $x$ contains a neighborhood $V$ of $x$ such that the inclusion map $V \to U$ is null-homotopic.
 

theorems/T000867.md

@@ -6,4 +6,4 @@ then:
   P000224: true
 ---
 
-Immediate by the definitions.
+Immediate from the definitions.

theorems/T000868.md

@@ -6,4 +6,4 @@ then:
   P000225: true
 ---
 
-Immediate by the definitions.
+Immediate from the definitions.

theorems/T000869.md

@@ -6,4 +6,4 @@ then:
   P000230: true
 ---
 
-A contractible space is simply connected.
+By {T583}.

theorems/T000870.md

@@ -6,4 +6,4 @@ then:
   P000231: true
 ---
 
-A contractible space is simply connected.
+By {T583}.