English

On two questions on selectively highly divergent spaces

General Topology 2023-11-03 v3

Abstract

A topological space XX is selectively highly divergent (SHD) if for every sequence of non-empty open subsets {Un:nω}\{U_n: n\in \omega \} of XX, we can pick a point xnUnx_n\in U_n, for every n<ωn<\omega, such that the sequence {xn:nω}\{x_n: n\in\omega\} has no convergent subsequences. In this note we answer four questions related to this notion asked in ArXiv:2307.11992.

Keywords

Cite

@article{arxiv.2309.11954,
  title  = {On two questions on selectively highly divergent spaces},
  author = {Angelo Bella and Santi Spadaro},
  journal= {arXiv preprint arXiv:2309.11954},
  year   = {2023}
}

Comments

6 pages, no figures

R2 v1 2026-06-28T12:28:09.988Z