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hal-00373427, version 1

Continuity of separately continuous group actions in p-spaces

Ahmed Bouziad () 1

Topology and its Applications 71, Issue 2 (1996) 119-124

Résumé : 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 be a a q-point of Y. We show that: (i) ƒ is strongly quasicontinuous at each point of X × {y}, (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.

  • 1 :  Laboratoire de Mathématiques Raphaël Salem (LMRS)
  • CNRS : UMR6085 – Université de Rouen
  • Domaine : Mathématiques/Topologie générale
  • Mots-clés : p-space – q-space – Separate continuity – Group action – Strong quasicontinuity – Subcontinuity – Semitopological group
 
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  • Contributeur : Ahmed Bouziad <>
  • Soumis le : Dimanche 5 Avril 2009, 16:41:45
  • Dernière modification le : Dimanche 5 Avril 2009, 16:41:45