Abstract

The class of spaces in the title (denoted by Haus(e-comp)) is introduced and it is compared with other classes of weak Hausdorff spaces. An explicit description of the Haus(e-comp)- epimorphisms is given by means of a variation of Arhangel'skii–Franklin's compactly determined closure. It is shown that Haus(e-comp) is not co-well-powered.

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