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- W2111095034 abstract "Abstract A Hausdorff space X is said to be compactly generated (a k-space) if and only if the open subsets U of X are precisely those subsets for which K ∩ U is open in K for all compact subsets of K of X . We interpret this property as a duality property of the lattice O ( X ) of open sets of X . This view point allows the introduction of the concept of being quasicompactly generated for an arbitrary sober space X . The methods involve the duality theory of up-complete semilattices, and certain inverse limit constructions. In the process, we verify that the new concept agrees with the classical one on Hausdorff spaces." @default.
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- W2111095034 date "1984-04-01" @default.
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- W2111095034 title "On the order-theoretical foundation of a theory of quasicompactly generated spaces without separation axiom" @default.
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- W2111095034 doi "https://doi.org/10.1017/s1446788700024654" @default.
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