A pair of spaces of upper semi-continuous maps and continuous maps (Q880144)
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scientific article; zbMATH DE number 5151662
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A pair of spaces of upper semi-continuous maps and continuous maps |
scientific article; zbMATH DE number 5151662 |
Statements
A pair of spaces of upper semi-continuous maps and continuous maps (English)
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10 May 2007
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The main result of this paper is the following: For a Tychonoff space \(X\) the following conditions are equivalent: a) \(X\) is a compactum and the set of isolated points is not dense in \(X\); b) \(\downarrow C(X)\) is homeomorphic to \(c_0 \); c) \((\downarrow USC(X), \downarrow C(X))\) is homeomorphic to \((Q, c_0 )\). This is a generalization of the results obtained by the first author in [Topology Appl. 153, 2908-2921 (2006; Zbl 1111.54008)] for metric spaces to Tychonoff spaces.
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Hibert cube
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Continuous map
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Hyperspace
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Regions below
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Upper semi-continuous
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Vietoris topology
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