Implications

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 157
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
1 \(\Rightarrow\) 157

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.

157:

Theorem of Goodner: A compact \(T_{2}\) space is extremally disconnected (the closure of every open set is open) if and only if each non-empty subset of \(C(X)\) (set of continuous real valued functions on \(X\)) which is pointwise bounded has a supremum.

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