add subcompact

Author: StevenClontz

properties/P000234.md

@@ -0,0 +1,14 @@
+---
+uid: P000234
+name: Subcompact
+---
+
+*from discussion at STDC, will add refs later*
+
+There exists a basis $\mathcal B$ of nonempty sets
+such that for every regular filter base
+$\mathcal F\subseteq\mathcal B$, $\bigcap\mathcal F\not=\emptyset$.
+
+A regular filter base $\mathcal F$ has the property that for each
+$A,B\in\mathcal F$, there exists $C\in\mathcal F$ such that
+$\operatorname{cl}(C)\subseteq A\cap B$.