Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 125
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 125

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

Howard-Rubin Number Statement
1:

\(C(\infty,\infty)\):  The Axiom of Choice: Every  set  of  non-empty sets has a choice function.

125:

There does not exist an infinite, compact connected \(p\) space. (A \(p\) space is a \(T_2\) space in which the intersection of any well orderable family of open sets is open.)

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