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- W138880596 abstract "The partially ordered collection of all Hausdorff topologies on a set is a complete upper semilattice; this semilattice always contains a maximum element (the discrete topology) but only contains a minimum element whenever the set is finite. When the set X is infinite, there are minimal elements in the semilattice. The minimal elements of the collection of all Hausdorff topologies on a set are called minimal Hausdorff topologies. A compact Hausdorff topology is minimal Hausdorff. In 1940, Katětov characterized those Hausdorff spaces which are minimal Hausdorff and produced an example of a minimal Hausdorff space which is not compact. The theory of the minimal elements of the semilattice of all Hausdorff topologies on a set is presented and developed in this paper." @default.
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- W138880596 date "1998-01-01" @default.
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- W138880596 title "Minimal Hausdorff Spaces — Then and Now" @default.
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