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On compact images of locally separable metric spaces. (English) Zbl 1072.54020

The author of the present paper is interested in the following question: How are compact images of locally separable metric spaces characterized? For this purpose, giving an internal characterization of sequentially-quotient compact image of locally separable metric spaces, he proves 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. Moreover, as an interesting application of the above result, the following is obtained: a space \(X\) is a quotient compact image of a locally separable metric space iff \(X\) is a pseudo-sequence-covering quotient compact image of a locally separable metric space, which is an affirmative answer to a question posed by Y. Ikeda in [Quest. Answers Gen. Topology 17, No. 2, 269–279 (1999; Zbl 0939.54014)].

MSC:

54E40 Special maps on metric spaces
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D50 \(k\)-spaces
54D55 Sequential spaces

Citations:

Zbl 0939.54014
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