A note on K-spaces

Authors

  • H. Wang
  • W. He

Keywords:

K-space, topological group, semitopological group, metrizable,

Abstract

In this paper, it is shown that every compact Hausdorff \(K\)-space has countable tightness. This result gives a positive answer to a problem posed by Malykhin and Tironi [‘Weakly Fréchet–Urysohn and Pytkeev spaces’, Topology Appl. \(104\) (2000), 181–190]. We show that a semitopological group \(G\) that is a \(K\)-space is first countable if and only if \(G\) is of point-countable type. It is proved that if a topological group \(G\) is a \(K\)-space and has a locally paracompact remainder in some Hausdorff compactification, then \(G\) is metrisable. DOI: 10.1017/S0004972714000112

Published

2014-06-03

Issue

Vol. 90 No. 1 (2014)

Section

Articles
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