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| HAL : hal-00373427, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Topology and its Applications 71, Issue 2 (1996) 119-124 |
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| Continuity of separately continuous group actions in p-spaces |
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| Ahmed Bouziad 1 |
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| (1996) |
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| 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. |
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| 1 : | Laboratoire de Mathématiques Raphaël Salem (LMRS) |
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CNRS : UMR6085 – Université de Rouen |
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| Domaine | : | Mathématiques/Topologie générale |
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| p-space – q-space – Separate continuity – Group action – Strong quasicontinuity – Subcontinuity – Semitopological group |
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| hal-00373427, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00373427 | |
| oai:hal.archives-ouvertes.fr:hal-00373427 | |
| Contributeur : Ahmed Bouziad | |
| Soumis le : Dimanche 5 Avril 2009, 16:41:45 | |
| Dernière modification le : Dimanche 5 Avril 2009, 16:41:45 | |
