University of Science and Technology, Changsha
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 $\aleph_0$-subspaces) and metric spaces (resp. locally separable metric spaces) by means of compact-covering maps, 1-sequence-covering maps, compact maps, $\pi$-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.
Keywords: Weak-bases, sn-networks, compact-covering maps, 1-sequence-covering maps, compact maps.
Classification (MSC2000): 54E99; 54C10
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