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September 29, 2025Open Access

Resolvability in products and squares

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This research demonstrates resolvability outcomes in products of Hausdorff spaces, suggesting implications for cardinal characteristics.

If both topological spaces are Hausdorff with cardinality ω, then their product is maximally resolvable.
Under certain conditions, including GCH, the product space can be κ+-resolvable depending on the cardinality of the spaces involved.
If one space has countable cofinality and the other has the cofinality of the continuum, the product is ω-resolvable.
Exploring resolvability in products leads to insights about characterizing isolated cardinals and their interactions.

A. V. Lipin (2025) studied this question.

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