Implications

We have the following indirect implication of form equivalence classes:

36 \(\Rightarrow\) 154
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
36 \(\Rightarrow\) 343 On Loeb and weakly Loeb Hausdorff spaces, Tachtsis, E. 2000, Math. Japon.
343 \(\Rightarrow\) 154 Products of compact spaces and the axiom of choice II , Hall, E. 2002, Math. Logic Quart.

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

Howard-Rubin Number Statement
36:

Compact T\(_2\) spaces are Loeb. (A space is Loeb if the set of non-empty closed sets has a choice function.)

343:

A product of non-empty, compact \(T_2\) topological spaces is non-empty.

154:

Tychonoff's Compactness Theorem for Countably Many \(T_2\) Spaces: The product of countably many \(T_2\) compact spaces is compact.

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