Regularity of the category of Kelley spaces
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.
scientific article; zbMATH DE number 854352