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Weak-bases and D -spaces

Dennis K. Burke (2007)

Commentationes Mathematicae Universitatis Carolinae

It is shown that certain weak-base structures on a topological space give a D -space. This solves the question by A.V. Arhangel’skii of when quotient images of metric spaces are D -spaces. A related result about symmetrizable spaces also answers a question of Arhangel’skii. Theorem.Any symmetrizable space X is a D -space ( hereditarily ) . Hence, quotient mappings, with compact fibers, from metric spaces have a D -space image. What about quotient s -mappings? Arhangel’skii and Buzyakova have shown that...

Weakly complete semimetrizable spaces and complete metrizability.

Salvador Romaguera, Sam D. Shore (1996)

Extracta Mathematicae

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,...

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