Implications

We have the following indirect implication of form equivalence classes:

354 \(\Rightarrow\) 350
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
354 \(\Rightarrow\) 32 Disasters in metric topology without choice, Keremedis, K. 2002, Comment. Math. Univ. Carolinae
32 \(\Rightarrow\) 350 clear

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
354:

A countable product of separable \(T_2\) spaces is separable.

32:

\(C(\aleph_0,\le\aleph_0)\): Every denumerable set of non-empty countable sets  has a choice function.

350:

\(MC(\aleph_0,\aleph_0)\): For every denumerable set \(X\) of non-empty denumerable sets there is a function \(f\) such that for all \(x\in X\), \(f(x)\) is a finite, non-empty subset of \(x\).

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