×

zbMATH — the first resource for mathematics

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

MSC:
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.)
PDF BibTeX XML Cite
Full Text: EuDML