Sequence-covering cs-images of metric spaces (Q2707052)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sequence-covering cs-images of metric spaces |
scientific article |
Statements
16 August 2001
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sequence-covering maps
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sequential spaces
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compact-countable collections
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\(cs\)-networks
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\(cs^*\)-networks
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weak bases
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\(cs\)-map
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Sequence-covering cs-images of metric spaces (English)
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This paper gives a characterization of a sequence-covering and (quotient) \(cs\)-image of a metric space by means of compact-countable \(cs\)-networks, and some analogous characterizations by means of compact-countable \(cs^*\)-networks (or weak bases). Here, a map \(f: X\to Y\) is called sequence-covering if each convergent sequence of \(Y\) is the image of some convergent sequence of \(X\), and \(f\) is called a \(cs\)-map if for any compact subset \(C\) of \(Y\), \(f^{-1}(C)\) is separable.
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