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Continuity of separately continuous group actions in p-spaces

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
71
Issue
2
Identifiers
DOI: 10.1016/0166-8641(95)00039-9
Keywords
  • P-Space
  • Q-Space
  • Separate Continuity
  • Group Action
  • Strong Quasicontinuity
  • Subcontinuity
  • Semitopological Group
Disciplines
  • Mathematics

Abstract

Abstract Let ƒ:X × Y → Z be a separately continuous mapping, where X is a Baire p-space and Z a completely regular space, and let y ϵ Y be a q-point. We show that 1. (i) ƒis strongly quasicontinuous at each point of X × { y}, 2. (ii) if Z is a p-space, then ƒ is subcontinuous at each point of A × { y}, where A is a dense subset of X. Then, we use (i) and (ii) to prove that every separately continuous action of a left topological group, which is a Baire p-space, in a p-space, is a continuous action. In particular, every semitopological group, which is a Baire p-space, has a continuous multiplication.

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