We have the following indirect implication of form equivalence classes:
Implication | Reference |
---|---|
384 \(\Rightarrow\) 14 |
"Maximal filters, continuity and choice principles", Herrlich, H. 1997, Quaestiones Math. |
14 \(\Rightarrow\) 154 |
Kategoriesatze und multiples Auswahlaxiom, Brunner, N. 1983c, Z. Math. Logik Grundlagen Math. |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
---|---|
384: | Closed Filter Extendability for \(T_1\) Spaces: Every closed filter in a \(T_1\) topological space can be extended to a maximal closed filter. |
14: | BPI: Every Boolean algebra has a prime ideal. |
154: | Tychonoff's Compactness Theorem for Countably Many \(T_2\) Spaces: The product of countably many \(T_2\) compact spaces is compact. |
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