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October 18, 2025Open Access

Constructing crowded Hausdorff P-spaces in set theory without the axiom of choice

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Novel results reveal properties of Hausdorff zero-dimensional P-spaces in set theory, suggesting implications of the axiom of choice.

A non-empty Hausdorff, crowded zero-dimensional P-space exists under specific conditions.
If X is uncountable, S(X, [X]^{≤ω}) proves to be a crowded zero-dimensional Hausdorff space.
The axiom of countable choice is linked with properties of P-spaces related to Dedekind-finite sets.
Relevant independence results highlight the interplay between the axiom of choice and topological properties.

Tachtsis et al. (2025) studied this question.

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