A better framework for first countable spaces

• Preuss, Gerhard ^[1]
  1. [1] Free University Berlin
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 4, Nº. 2, 2003, págs. 289-299
• Idioma: inglés
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• Resumen

  • In the realm of semiuniform convergence spaces first countability is divisible and leads to a well-behaved topological construct with natural function spaces and one-point extensions such that countable products of quotients are quotients. Every semiuniform convergence space (e.g. symmetric topological space, uniform space, filter space, etc.) has an underlying first countable space. Several applications of first countability in a broader context than the usual one of topological spaces are studied.