A note on spaces with locally countable weak-bases

Li, Zhaowen and Li, Xiaomin (2007) A note on spaces with locally countable weak-bases. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 23 (2). pp. 167-175. ISSN 0866-0174

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Abstract

In this paper, we show that a regular space with a locally countable weak-base is g-metrizable. Secondly, we establish the relationships between spaces with a locally countable weak-base (resp. spaces with a locally countable weak-base consisting of ℵ0-subspaces) and metric spaces (resp. locally separable metric spaces) by means of compact-covering maps, 1-sequence-covering maps, compact maps, π-maps and ss-maps, and show that all these characterizations are mutually equivalent. Thirdly, we show that 1-sequence-covering, quotient, ss-maps preserve spaces with a locally countable weak base.

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