Regularity of the category of Kelley spaces (Q1909229)
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scientific article; zbMATH DE number 854352
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Regularity of the category of Kelley spaces |
scientific article; zbMATH DE number 854352 |
Statements
Regularity of the category of Kelley spaces (English)
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1 July 1996
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It is well known that, although the category of all topological spaces has image factorizations, it fails to be regular because quotient maps are not stable under pullback. In this short note, the authors prove that the category of Hausdorff \(k\)-spaces is regular, by an ingenious argument making use of its Cartesian closedness.
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regularity
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Kelley spaces
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category of topological spaces
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category of Hausdorff \(k\)-spaces
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stable under pullback
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Cartesian closedness
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