On \((\beta,G_{\Pi})\)-unfavourable spaces

Authors

  • H. Wang
  • W. He
  • J. Zhang

Keywords:

G game, (, G)-unfavorable, strategy, topological group

Abstract

To study when a paratopological group becomes a topological group, A. V. Arhangel'skii et al. introduced the class of (;G)-unfavorable spaces. In this paper we show that every -complete (resp. normal) (;G)-unfavorable semitopological group is a topological group. It is proved that the product of a (;G)-unfavorable space and a strongly Frechet (;G)-favorable space is (;G)-unfavorable. We also show that continuous closed irreducible mappings preserve the (;G)-unfavorableness in both directions. Some of other properties of (;G)-unfavorable spaces are studied.

Published

2020-08-08

Issue

Vol. 102 No. 3 (2020)

Section

Articles
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