Basically disconnected and Tychonoff implies sequentially discrete (#1440)

Author: Moniker1998

theorems/T000787.md

@@ -0,0 +1,14 @@
+---
+uid: T000787
+if:
+  and:
+  - P000085: true
+  - P000006: true
+then:
+  P000167: true
+refs:
+  - mathse: 4751804
+    name: Answer to "What separation is required to ensure extremally disconnected spaces are sequentially discrete?"
+---
+
+Since $X$ is {P6}, in the proof of {{mathse:4751804}} we can take $U_n$ to be cozero sets. Then $U = \bigcup_n U_{2n}$ and $V = \bigcup_n U_{2n+1}$ are open disjoint cozero sets with $x\in \overline{U}\cap \overline{V}$, which contradicts that $X$ is basically disconnected.