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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.)
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