English

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}
}
R2 v1 2026-07-01T05:59:14.888Z