1. Selective separability and $q^+$ on maximal spaces
- Author
-
de la Vega, Ramiro, Murgas, Javier, and Uzcátegui, Carlos
- Subjects
Mathematics - General Topology ,54G05, 54A35, 03E57 - Abstract
Given a hereditarily meager ideal $\mathcal{I}$ on a countable set $X$ we use Martin's axiom for countable posets to produce a zero-dimensional maximal topology $\tau^\mathcal{I}$ on $X$ such that $\tau^\mathcal{I}\cap \mathcal{I}=\{\emptyset\}$ and, moreover, if $\mathcal{I}$ is $p^+$ then $\tau^\mathcal{I}$ is selectively separable (SS) and if $\mathcal{I}$ is $q^+$, so is $\tau^\mathcal{I}$. In particular, we obtain regular maximal spaces satisfying all boolean combinations of the properties SS and $q^+$., Comment: 17 pages
- Published
- 2020