From 84c5b337d2d8616641d5cf8a331d97dcecc9fba0 Mon Sep 17 00:00:00 2001 From: Moniker1998 Date: Mon, 8 Sep 2025 07:43:31 +0200 Subject: [PATCH] added proof --- theorems/T000787.md | 14 ++++++++++++++ 1 file changed, 14 insertions(+) create mode 100644 theorems/T000787.md diff --git a/theorems/T000787.md b/theorems/T000787.md new file mode 100644 index 0000000000..b6d55b6820 --- /dev/null +++ b/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.