Geodesic
On Katětov Spaces
Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 425-433

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DOI

Recent work by Krystock, Porter, and Vermeer has emphasized the importance of the concepts of Katětov spaces and H-sets in the theory of H-closed spaces. These properties are closely related to being the θ-closure of some set and being the adherence of an open filter. This relationship is developed by establishing, among other facts, that an H-closed space in which every closed set is the θ-closure of some set is compact and the θ-closure of a subset of an H-closed space is Katětov and characterizing the open filter adhérences of a space as precisely those sets which are the image of a closed set of the absolute of the space. Also, examples are given of a countable, scattered space which is not Katětov and an H-closed space with an H-closed subspace which is not the θ-closure of any subset of the given space.
DOI : 10.4153/CMB-1989-061-0
Mots-clés : 54D25, 54C10 
Porter, Jack; Tikoo, Mohan. On Katětov Spaces. Canadian mathematical bulletin, Tome 32 (1989) no. 4, pp. 425-433. doi: 10.4153/CMB-1989-061-0
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     title = {On {Kat\v{e}tov} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {425--433},
     year = {1989},
     volume = {32},
     number = {4},
     doi = {10.4153/CMB-1989-061-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-061-0/}
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