Implications

We have the following indirect implication of form equivalence classes:

115 \(\Rightarrow\) 118
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
115 \(\Rightarrow\) 118 On Loeb and weakly Loeb Hausdorff spaces, Tachtsis, E. 2000, Math. Japon.

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

Howard-Rubin Number Statement
115:

The product of weakly Loeb \(T_2\) spaces is weakly Loeb. Weakly Loeb means the set of non-empty closed subsets has a multiple choice function.)

118:

Every linearly orderable topological space is normal.  Birkhoff [1967], p 241.

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