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

Voir la notice de l'article provenant de la source Cambridge University Press

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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[1] 1. Dickman, R. F., Jr., and J. R. Porter, 9-closed subsets of Hausdorff spaces, Pac. J. Math. 59 (1975), 407–415. Google Scholar

[2] 2. Dow, A. and J. R. Porter, Cardinalities of H-closed spaces, Topology Proc. 7 (1982), 27–50. Google Scholar

[3] 3. Herrlich, H., T-Abgeschlossenheit und Tv-Minimalität, Math. Zeit. 88 (1968), 285–294. Google Scholar

[4] 4. M. Katëtov, Über H-abgeschlossene und bikompakt Räume, Časopis pěst. mat. 69 (1940), 36–49. Google Scholar

[5] 5. Krystock, R. L., On H-sets and open filter adhérences, Canad. Math. Bull. 31 (1) (1988), 37–44. Google Scholar

[6] 6. Porter, J. R. and Vermeer, J., Spaces with coarser minimal Hausdorff topologies, Trans. Amer. Math. Soc. 289 (1985), 59–71. Google Scholar

[7] 7. Porter, J. R. and Woods, R. G., Extensions and absolutes of Hausdorff spaces, Springer-Verlag, New York, 1987. Google Scholar

[8] 8. Velicko, N. V., H-closed topological spaces, Amer. Math. Soc. Transi. 78 (1968), 103–118. Google Scholar

[9] 9. Vermeer, J., Closed subspaces of H-closed spaces, Pac. J. Math. 118 (1985), 229–247. Google Scholar

[10] 10. Viglino, G., C-compact spaces, Duke Math. J. 36 (1969), 761–764. Google Scholar

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