Uniformizable and realcompact bornological universes

• Vroegrijk, Tom ^[1]
  1. [1] University of Antwerp

     University of Antwerp

     Arrondissement Antwerpen, Bélgica

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 10, Nº. 2, 2009, págs. 277-287
• Idioma: inglés
• DOI: 10.4995/agt.2009.1740
• Enlaces
  • Texto completo
• Resumen

  • Bornological universes were introduced some time ago by Hu and obtained renewed interest in recent articles on convergence in hyperspaces and function spaces and optimization theory. One o fHu's results gives us a necessary and sufficient condition for which a bornological universe is metrizable. In this article we will extend thi sresult and give a characterization of uniformizable bornological universes. Furthermore, a construction on bornological universes that the author used to find the bornological dual of function spaces endowed with the bounded-open topology will be used to define realcompactness for bornological universes. We will also give various characterizations of this new concept.

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