Weakly complete semimetrizable spaces and complete metrizability.

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 -