# 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

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topRomaguera, 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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