Hereditary Coreflective Subcategories of Categories of Topological Spaces

摘要

Let 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 ? be a coreflective subcategory of . Extending the corresponding result obtained for coreflective subcategories of Top we prove that ? 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 ? of containing a non-discrete space is generated by a class of prime spaces and if is a quotient-reflective subcategory of Top, then the assignment 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 that contain . Some applications of these results in the categories of Hausdorff spaces, Tychonoff spaces and zero-dimensional Hausdorff spaces are presented.