On proximal fineness of topological groups in their right uniformity

• Bouziad, Ahmed ^[1]
  1. [1] University of Rouen

     University of Rouen

     Arrondissement de Rouen, Francia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 20, Nº. 2, 2019, págs. 419-430
• Idioma: inglés
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• Resumen

  • A uniform space X is said to be proximally fine if every proximally continuous function defined on X into an arbitrary uniform pace Y is uniformly continuous. We supply a proof that every topological group which is functionally generated by its precompact subsets is proximally fine with respect to its right uniformity. On the other hand, we show that there are various permutation groups G on the integers N that are not proximally fine with respect to the topology generated by the sets {g ∈ G : g(A) ⊂ B}, A, B ⊂ N.