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arXiv · 2509.22590

New examples in the study of selectively separable spaces

Alan Dow·Hayden Pecoraro
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Abstract

The property of being selectively separable is well-studied and generalizations such as H-separable and wH-separable have also generated much interest. Bardyla, Maesano, and Zdomskyy proved from Martin's Axiom that there are countable regular wH-separable spaces that are not H-separable. We prove there is a ZFC example. Their example was also Fr\'echet-Urysohn, and we produce two additional examples from weaker assumptions.

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Alan Dow, Hayden Pecoraro. 2025-09-26. New examples in the study of selectively separable spaces. https://arxiv.org/abs/2509.22590

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