Implications

We have the following indirect implication of form equivalence classes:

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

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

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

Howard-Rubin Number Statement
353:

A countable product of first countable spaces is first countable.

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 \(x\).

Comment:

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