Implications

We have the following indirect implication of form equivalence classes:

302 \(\Rightarrow\) 300
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
302 \(\Rightarrow\) 301 Some propositions equivalent to the Sikorski extension theorem for Boolean algebras, Bell, J.L. 1988, Fund. Math.
301 \(\Rightarrow\) 300 Some propositions equivalent to the Sikorski extension theorem for Boolean algebras, Bell, J.L. 1988, Fund. Math.

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.

301:

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

300:

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

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