English

Countable tightness is not discretely reflexive in $\sigma$-compact spaces

General Topology 2024-11-08 v1

Abstract

Answering a question raised by V. V. Tkachuk, we present several examples of σ\sigma-compact spaces, some only consistent and some in ZFC, that are not countably tight but in which the closure of any discrete subset is countably tight. In fact, in some of our examples the closures of all discrete subsets are even first countable.

Keywords

Cite

@article{arxiv.2411.04523,
  title  = {Countable tightness is not discretely reflexive in $\sigma$-compact spaces},
  author = {István Juhász and Jan van Mill},
  journal= {arXiv preprint arXiv:2411.04523},
  year   = {2024}
}

Comments

7 pages

R2 v1 2026-06-28T19:51:05.462Z