On cs-mappings (Q2748330)
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scientific article; zbMATH DE number 1659211
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On cs-mappings |
scientific article; zbMATH DE number 1659211 |
Statements
23 April 2002
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compact-covering mapping
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\(k\)-network
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metrizable space
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cs-mapping
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On cs-mappings (English)
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Let \(f:X\to Y\) be a continuous and onto mapping \(f\) is called a cs-mapping if for any compact subset \(C\) of \(Y\), \(f^{-1}(C)\) is separable in \(X\). In this paper, it is showed that a space \(X\) has a compact-countable network if and only if \(X\) is a cs-image of a metric space. But a result about a compact-covering cs-image of a metric space does not hold. A real characterization of a compact-covering cs-image of a metric space is obtained by \textit{J. Li} and \textit{S. Jiang} [Indian J. Pure Math. 32, No. 2, 285-288 (2001; Zbl 0982.54030)].
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