The aim of this paper is to investigate closed hereditary coreflective subcategories in epireflective subcategories A of Top, mainly in the case that ZD ⊆ A ⊆ Tych. Particularly the closed hereditary coreflective hull of the one-point compactification of the discrete space on the set of all non-negative integers in such epireflective subcategories is studied. It is proved that under some set-theoretic assumptions it is the whole category A.
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