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• W3103297450 startingPage "2061" @default.
• W3103297450 abstract "Let (X,?) be a Hausdorff space, where X is an infinite set. The compact complement topology ?* on X is defined by: ?* = {0}?{XM:M is compact in (X,?)}. In this paper, properties of the space (X,?*) are studied in ZF and applied to a characterization of k-spaces, to the Sorgenfrey line, to some statements independent of ZF, as well as to partial topologies that are among Delfs-Knebusch generalized topologies. Between other results, it is proved that the axiom of countable multiple choice (CMC) is equivalent with each of the following two sentences: (i) every Hausdorff first-countable space is a k-space, (ii) every metrizable space is a k-space. A ZF-example of a countable metrizable space whose compact complement topology is not first-countable is given." @default.
• W3103297450 created "2020-11-23" @default.
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• W3103297450 date "2019-01-01" @default.
• W3103297450 modified "2023-10-18" @default.
• W3103297450 title "Compact complement topologies and k-spaces" @default.
• W3103297450 cites W1541012876 @default.
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• W3103297450 doi "https://doi.org/10.2298/fil1907061k" @default.
• W3103297450 hasPublicationYear "2019" @default.
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