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Selective separability and $q^+$ on maximal spaces
- Publication Year :
- 2020
-
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 $q^+$.<br />Comment: 17 pages
- Subjects :
- Mathematics - General Topology
54G05, 54A35, 03E57
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2001.07156
- Document Type :
- Working Paper