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

Dikranjan, D.; Giuli, E.

Commentat. Math. Univ. Carol. 27, 395-417 (1986).

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.)

Keywords:

weak Hausdorff spaces; epimorphisms; ordinal invariants; A-closure; co- well-poweredness