On relatively normal spaces, relatively regular spaces, and on relative property \((a)\) (Q1292715)
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scientific article; zbMATH DE number 1307858
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On relatively normal spaces, relatively regular spaces, and on relative property \((a)\) |
scientific article; zbMATH DE number 1307858 |
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On relatively normal spaces, relatively regular spaces, and on relative property \((a)\) (English)
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26 December 2000
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The following results concerning relative topological properties are proved: (1) A regular (Tychonoff) space \(Y\) is normal in every larger regular (Tychonoff) space if and only if \(Y\) is Lindelöf or normal almost compact. (2) A functionally Hausdorff space \(Y\) is regular in every larger functionally Hausdorff space if and only if \(Y\) is compact. (3) A Hausdorff (regular, Tychonoff) space \(Y\) is relatively (a) in every larger Hausdorff (regular, Tychonoff) space \(X\) if and only if \(Y\) is compact.
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relative topological properties
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almost compact
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