Generalized separability in vector-valued function spaces (Q2714170)
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scientific article; zbMATH DE number 1603959
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Generalized separability in vector-valued function spaces |
scientific article; zbMATH DE number 1603959 |
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12 June 2001
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continuous maps
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Generalized separability in vector-valued function spaces (English)
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Let \(X\) be a completely regular Hausdorff space and let \(E\) be a Hausdorff topological vector space. The paper treats the so-called neighbourhood separability in the function spaces \(C(X,E)\), \(C_b(X,E)\) and \(C_0(X,E)\) (equipped with different topologies) without the condition of local convexity of \(E\). In fact, instead of local convexity, the author considers the more general situation when \(E\) is semi-convex. Examples to show the applicability of the results are also presented.
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