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- W4364858245 abstract "We introduce the class of linearly S-closed spaces as a proper subclass of linearly H-closed spaces. This property lies between S-closedness and countable S-closedness. A space is called linearly S-closed if and only if any semi-open chain cover posses a member dense in the space. It is shown that in the class of extremally disconnected spaces the class of linearly H-closed spaces and linearly S-closed spaces coincide. We gave characterizations of these spaces in terms of s-accumulation points of chain filter bases and complete s-accumulation points of families of open subsets. While regular S-closed spaces are compact there is a non compact, regular, linearly S-closed space. It is shown that a Hausdorff, first countable, linearly S-closed space is extremally disconnected. Moreover, in the class of first countable, regular, compact spaces the notions of S-closedness, linearly S-closedness and extremally disconnectedness are equivalent. Some cardinality bounds for this class of spaces are obtained. Several examples are provided to illustrate our results." @default.
- W4364858245 created "2023-04-13" @default.
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- W4364858245 date "2022-01-01" @default.
- W4364858245 modified "2023-09-26" @default.
- W4364858245 title "Linearly S-closed spaces" @default.
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- W4364858245 doi "https://doi.org/10.2298/fil2220841s" @default.
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