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The Kuratowski-Mrówka characterization and weak forms of compactnessKeywords: kuratowski-mrówka characterization of compact spaces, closure operator, weak form of compactness. Abstract: for cardinals κ>\aleph0, characterizations of the kuratowski-mrówka type of initial κ-compactness and final κ-compactness are given. moreover, a categorical characterization of κ-compactness is given in terms of a closure operator depending on an ultrafilter over κ.
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