Weakly complete semimetrizable spaces and complete metrizability.
Romaguera, Salvador ; Shore, Sam D.
Extracta Mathematicae, Tome 11 (1996), p. 276-281 / Harvested from Biblioteca Digital de Matemáticas

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.

Publié le : 1996-01-01
DMLE-ID : 1280
@article{urn:eudml:doc:38463,
     title = {Weakly complete semimetrizable spaces and complete metrizability.},
     journal = {Extracta Mathematicae},
     volume = {11},
     year = {1996},
     pages = {276-281},
     zbl = {0881.54034},
     mrnumber = {MR1437451},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38463}
}
Romaguera, Salvador; Shore, Sam D. Weakly complete semimetrizable spaces and complete metrizability.. Extracta Mathematicae, Tome 11 (1996) pp. 276-281. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38463/