Abstract
In [1] the following problems were listed as open: Problem 14. Is a regular space in which every closed subset is regular-closed compact? Problem 15. Is a Urysohn-space in which every closed subset is Urysohnclosed compact? To answer the question for Hausdorff-closed spaces in the affirmative, M. H. Stone [12] used Boolean rings and M. Katˇetov [10] used topological methods. In this article, all three questions are answered affirmatively using filters.
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