Implications

We have the following indirect implication of form equivalence classes:

302 \(\Rightarrow\) 397
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
302 \(\Rightarrow\) 392 clear
392 \(\Rightarrow\) 394 clear
394 \(\Rightarrow\) 397 clear

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

Howard-Rubin Number Statement
302:

Any continuous surjection between compact Hausdorff spaces has an irreducible restriction to a closed subset of its domain.

392:

\(C(LO,LO)\): Every linearly ordered set of linearly orderable sets has a choice function.

394:

\(C(WO,LO)\): Every well ordered set of non-empty linearly orderable sets has a choice function.

397:

\(MC(WO,LO)\): For each well ordered family of non-empty linearly orderable sets \(X\), there is a function \(f\) such that for all \(x\in X\) \(f(x)\) is a non-empty, finite subset of \(x\).

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