Implications

We have the following indirect implication of form equivalence classes:

354 \(\Rightarrow\) 5
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 \(\Rightarrow\) 5 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.

5:

\(C(\aleph_0,\aleph_0,\Bbb R)\): Every denumerable set of non-empty denumerable subsets of \({\Bbb R}\) has a choice function.

Comment:

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