Ordinal invariants and epimorphisms in some categories of weak Hausdorff spaces. (English) Zbl 0627.54005

For various classes \({\mathcal P}\) of topological spaces the category Haus(\({\mathcal P})\) of all spaces where continuous images of \({\mathcal P}\)- members are Hausdorff subspaces, is discussed. Epimorphisms are characterized, and examples given to show that Haus(\({\mathcal P})\) can be, and can fail to be, co-well-powered. Epimorphisms are also studied in the category \({\mathcal P}_ 3\) of all spaces X where continuous pre-images in \({\mathcal P}\)-members of the diagonal in \(X\times X\) are closed. It is shown that Haus(\({\mathcal P})\) often is a subcategory of \({\mathcal P}_ 3\). Certain ordinal and cardinal invariants are also discussed, relating to the co- well-poweredness of Haus(\({\mathcal P})\).
Reviewer: E.Eugenes


54B30 Categorical methods in general topology
18B30 Categories of topological spaces and continuous mappings (MSC2010)
18A35 Categories admitting limits (complete categories), functors preserving limits, completions
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
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