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Countable + P space => Alexandrov#1776

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Countable + P space => Alexandrov#1776
felixpernegger wants to merge 3 commits into
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countablepspacealexandriv

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@felixpernegger felixpernegger commented May 17, 2026

We need this theorem for P-space => $\alpha_1$. (both theorems do not actually give new traits but we should have them for completeness, see this) comment.

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prabau commented May 17, 2026

The theorem also works with countable replaced by locally countable.

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thanks

@felixpernegger felixpernegger marked this pull request as draft May 17, 2026 04:06
@felixpernegger felixpernegger added the awaiting-author This PR requires the author to take further action in order to continue. label May 17, 2026
@felixpernegger felixpernegger removed the awaiting-author This PR requires the author to take further action in order to continue. label May 17, 2026
@felixpernegger felixpernegger marked this pull request as ready for review May 17, 2026 04:14
Comment thread theorems/T000894.md

Let $x \in X$, $A$ be the neighborhood kernel of $x$ and, by {P93}, $V$ be a countable open neighborhood of $x$.

If $V=A$ we are clearly done.
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Note this case distinction is actually necessary for $\bigcap S = A$ to hold

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