English

Selective separability and $q^+$ on maximal spaces

General Topology 2020-01-22 v1

Abstract

Given a hereditarily meager ideal I\mathcal{I} on a countable set XX we use Martin's axiom for countable posets to produce a zero-dimensional maximal topology τI\tau^\mathcal{I} on XX such that τII={}\tau^\mathcal{I}\cap \mathcal{I}=\{\emptyset\} and, moreover, if I\mathcal{I} is p+p^+ then τI\tau^\mathcal{I} is selectively separable (SS) and if I\mathcal{I} is q+q^+, so is τI\tau^\mathcal{I}. In particular, we obtain regular maximal spaces satisfying all boolean combinations of the properties SS and q+q^+.

Keywords

Cite

@article{arxiv.2001.07156,
  title  = {Selective separability and $q^+$ on maximal spaces},
  author = {Ramiro de la Vega and Javier Murgas and Carlos Uzcátegui},
  journal= {arXiv preprint arXiv:2001.07156},
  year   = {2020}
}

Comments

17 pages

R2 v1 2026-06-23T13:15:43.179Z