Weakly complete semimetrizable spaces and complete metrizability.

Salvador Romaguera; Sam D. Shore

Extracta Mathematicae (1996)

  • Volume: 11, Issue: 2, page 276-281
  • ISSN: 0213-8743

Abstract

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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.

How to cite

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Romaguera, Salvador, and Shore, Sam D.. "Weakly complete semimetrizable spaces and complete metrizability.." Extracta Mathematicae 11.2 (1996): 276-281. <http://eudml.org/doc/38463>.

@article{Romaguera1996,
abstract = {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.},
author = {Romaguera, Salvador, Shore, Sam D.},
journal = {Extracta Mathematicae},
keywords = {Espacio metrizable compacto; Espacio topológico; Espacio paracompacto; o-metric; asymmetric; completeness; weakly completely asymmetrizable space},
language = {eng},
number = {2},
pages = {276-281},
title = {Weakly complete semimetrizable spaces and complete metrizability.},
url = {http://eudml.org/doc/38463},
volume = {11},
year = {1996},
}

TY - JOUR
AU - Romaguera, Salvador
AU - Shore, Sam D.
TI - Weakly complete semimetrizable spaces and complete metrizability.
JO - Extracta Mathematicae
PY - 1996
VL - 11
IS - 2
SP - 276
EP - 281
AB - 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.
LA - eng
KW - Espacio metrizable compacto; Espacio topológico; Espacio paracompacto; o-metric; asymmetric; completeness; weakly completely asymmetrizable space
UR - http://eudml.org/doc/38463
ER -

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