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Basically disconnected and Tychonoff implies sequentially discrete #1440

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Merged
prabau merged 1 commit into from
Sep 8, 2025
Merged

Basically disconnected and Tychonoff implies sequentially discrete #1440

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14 changes: 14 additions & 0 deletions theorems/T000787.md
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---
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.