Countability properties of the \(\sigma\)-compact-open topology on \(C^*(X)\) (Q2850625)
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scientific article; zbMATH DE number 6212831
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Countability properties of the \(\sigma\)-compact-open topology on \(C^*(X)\) |
scientific article; zbMATH DE number 6212831 |
Statements
27 September 2013
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function space
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separability
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\(\aleph_{0}\)-bounded
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the countable chain condition
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Lindelöf
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cosmic
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second countable
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Countability properties of the \(\sigma\)-compact-open topology on \(C^*(X)\) (English)
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Let \(X\) be a Tychonoff space and \(C_{\sigma}^{*}(X)\) be the set of all bounded real-valued continuous functions on \(X\) endowed with the \(\sigma\)-compact-open topology. In this work, the authors study the separability, \(\aleph_{0}\)-boundedness, countable chain condition, second countability, and Lindelöf property of \(C_{\sigma}^{*}(X)\).
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