We have the following indirect implication of form equivalence classes:

128 \(\Rightarrow\) 128
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
128 \(\Rightarrow\) 128 Realisierung und Auswahlaxiom, Brunner, N. 1984f, Arch. Math. (Brno)

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

Howard-Rubin Number Statement
128:

Aczel's Realization Principle: On every infinite set there is a Hausdorff topology with an infinite set of non-isolated points.

128:

Aczel's Realization Principle: On every infinite set there is a Hausdorff topology with an infinite set of non-isolated points.

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