New examples in the study of selectively separable spaces
General Topology
2025-10-22 v2
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.
Keywords
Cite
@article{arxiv.2509.22590,
title = {New examples in the study of selectively separable spaces},
author = {Alan Dow and Hayden Pecoraro},
journal= {arXiv preprint arXiv:2509.22590},
year = {2025}
}