Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 134
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 134

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.

134:

If \(X\) is an infinite \(T_1\) space and \(X^{Y}\) is \(T_5\), then \(Y\) is countable. (\(T_5\) is 'hereditarily \(T_4\)'.)

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