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Let A be an epireflective subcategory of the category Top of topological spaces that is not bireflective (e.g., the category of Hausdorff spaces, the category of Tychonoff spaces) and B be a coreflective subcategory of A. Extending the corresponding result obtained for coreflective subcategories of Top we prove that B is hereditary if and only if it is closed under the formation of prime factors. As a consequence we obtain that every hereditary coreflective subcategory B of A containing a non-discrete space is generated by a class of prime spaces and if A is a quotientreflective subcategory of Top, then the assignment B → B ∩ A gives a bijection of the collection of all hereditary coreflective subcategories of Top that contain the class FG of all finitely generated spaces onto the collection of all hereditary coreflective subcategories of A that contain FG ∩ A. Some applications of these results in the categories of Hausdorff spaces, Tychonoff spaces and zerodimensional Hausdorff spaces are presented. (2000): 18D15, 54B30. Mathematics Subject Classifications

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