Notes on \(𝐾\)-topological groups and homeomorphisms of topological groups

Authors

  • Hanfeng Wang
  • Wei He

Abstract

In this paper, it is showed that there exists a connected topological group which is not homeomorphic to any ðœ”-narrow topological group, and also that there exists a zero-dimensional topological group ðº with neutral element ð‘’ such that the subspace ð‘‹ = ðº ∖ {ð‘’} is not homeomorphic to any topological group. These two results give negative answers to two open problems in [1] respectively. We show that if a compact topological group is a ð¾-space, then it is metrizable. This result gives an affirmative answer to a question posed by V.I.Malykhin in the category of topological groups. We also prove that a regular ð¾-space ð‘‹ is a Weakly Fr´echet-Urysohn space if and only if ð‘‹ has countable tightness. 10.1017/S0004972712000561

Published

2013-04-29

Issue

Vol. 87 No. 3 (2013)

Section

Articles
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