Implications

• Implications Home
• Code 1 Implications
• Code 2 Implications
• Code 3 Implications
• Code 4 Implications
• Code 5 Implications
• Code 6 Implications
• Complete List
• Search

We have the following indirect implication of form equivalence classes:

181 $\Rightarrow$ 353 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
181 $\Rightarrow$ 8	clear
8 $\Rightarrow$ 353	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
181:	$C(2^{\aleph_0},\infty)$: Every set $X$ of non-empty sets such that $|X|=2^{\aleph_0}$ has a choice function.
8:	$C(\aleph_{0},\infty)$:
353:	A countable product of first countable spaces is first countable.

Comment: