The Alexandroff property and the preservation of strong uniform continuity

• Beer, Gerald ^[1]
  1. [1] California State University Los Angeles

     California State University Los Angeles

     Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 11, Nº. 2, 2010, págs. 117-133
• Idioma: inglés
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• Resumen

  • In this paper we extend the theory of strong uniform continuity and strong uniform convergence, developed in the setting of metric spaces in, to the uniform space setting, where again the notion of shields plays a key role. Further, we display appropriate bornological/variational modifications of classical properties of Alexandroff [1] and of Bartle for nets of continuous functions, that combined with pointwise convergence, yield continuity of the limit for functions between metric spaces.