Implications

We have the following indirect implication of form equivalence classes:

384 \(\Rightarrow\) 371
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
384 \(\Rightarrow\) 14 "Maximal filters, continuity and choice principles", Herrlich, H. 1997, Quaestiones Math.
14 \(\Rightarrow\) 371 S´eminaire d’Analyse 1994, Morillon, 1993,

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.

371:

There is an infinite, compact, Hausdorff, extremally disconnected topological space.  Morillon [1993].

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