Weakly complete semimetrizable spaces and complete metrizability

• Autores: Salvador Romaguera Bonilla , Sam D. Shore
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 11, Nº 2, 1996, págs. 276-281
• Idioma: inglés
• Títulos paralelos:
  • Espacios semimetrizables débilmente completos y metrizabilidad completa
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• Resumen

  • In [4], J. Ceder proved that every paracompact strongly complete semimetrizable space is completely metrizable. This result cannot be generalized to paracompact weakly complete semimetrizable spaces as a known example of L. F. McAuley shows (see [11, Theorem 3.2]). It then arises, in a natural way, the question of obtaining conditions for the complete metrizability of a paracompact weakly complete semimetrizable space. In this note we give an answer to this question. We show that every regular theta, weakly complete asymmetrizable space is a complete Aronszajn space and deduce, among other results, that every paracompact theta, weakly complete semimetrizable space is completely metrizable. Some examples related to the obtained results are also given.