Topological groups in which each nowhere dense subset is closed
type: Item
instance of: scholarly article
title: Topological groups in which each nowhere dense subset is closed
zbMATH Open document ID: 0916.22002
DOI: 10.1007/BF02310302
published in: Mathematical Notes
publication date: 1999-07-12T00:00:00Z
review text: It is proved under the combinatorial principle \(p=\mathfrak c\) (which is also called Booth lemma) that any nondiscrete metrizable group topology on an Abelian group can be strengthened to a nondiscrete group topology such that each nowhere dense subset is closed. Recall that the Martin's axiom (and therefore also the continuum hypothesis) implies the validity of the combinatorial principle \(p=\mathfrak c\).
Mathematics Subject Classification ID: 22A05
zbMATH DE Number: 1274232
zbMATH Keywords: Abelian group
zbMATH Keywords: metrizable topology
zbMATH Keywords: Booth lemma
zbMATH Keywords: continuum hypothesis
zbMATH Keywords: nowhere dense set
zbMATH Keywords: Martin's axiom
zbMATH Keywords: nondiscrete topology
author: Yevhen Zelenyuk
reviewed by: Václav Koubek
MaRDI profile type: Publication
cites work: Q3861618
cites work: Discrete subsets of topological groups
cites work: Absolutely decomposable groups
cites work: Q3483484
cites work: Q3662271
cites work: Topological groups with finite semigroups of ultrafilters
description: scientific article; zbMATH DE number 1274232