Topology Proceedings 27 No. 1 (2003), pp. 351-360

On compact images of locally separable metric spaces

Ge Ying

In this paper, we give a characterization of sequentially-quotient compact images of locally separable metric spaces to prove that a space X is a sequentially-quotient compact image of a locally separable metric space if and only if X is a pseudo-sequence-covering compact image of a locally separable metric space. As an application of the above result, we obtain that a space X is a quotient compact image of a locally separable metric space if and only if X is a pseudo-sequence-covering quotient compact image of a locally separable metric space, which answers a question posed by Y. Ikeda.

Keywords: compact mapping, locally separable metric space, point-star network, sequentially-quotient (pseudo-sequence-covering, subsequence-covering) mapping

Mathematics Subject Classification: 54C10 54D50 54D55 (54E99)

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Topology Proceedings, Volume 27 No. 1 (2003)
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