Fréchet quasi-bases and the closed images of metric spaces (Q2774182)
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scientific article; zbMATH DE number 1713443
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fréchet quasi-bases and the closed images of metric spaces |
scientific article; zbMATH DE number 1713443 |
Statements
27 June 2002
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Fréchet space
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sequential network
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closed mapping
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\(s\)-mapping
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Fréchet quasi-bases and the closed images of metric spaces (English)
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The concept of Fréchet quasi-bases is introduced by \textit{Shou Lin} in [Sequential networks and sequentially quotient images of metric spaces, Acta Math. Sin. 42, 49-54 (1999)]. In this paper, some new characterizations of certain closed images of metric spaces and locally separable metric spaces are obtained by the Fréchet quasi-bases. For example, a space \(X\) is a closed \(s\)-image of a metric space if and only if \(X\) is a space with a \(\sigma\)-locally finite Fréchet quasi-base.
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