Geodesic
ON H-Sets and Open Filter Adherences(1)
Canadian mathematical bulletin, Tome 31 (1988) no. 1, pp. 37-44

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DOI

The relationship between H-sets and open filter adhérences is considered. The open filter adhérences of an H-closed space are shown to be H-sets; and, a necessary and sufficient condition is given for an H-set S, of a Hausdorff space X, to be an open filter adherence. A necessary condition is determined for the existence of a minimal adherent set which contains S; and, in the case that X is H-closed, sufficient conditions are determined. As a related result, an H-closed space X is shown to be seminormal if every H-set of X possesses a neighborhood base consisting of regular open sets.
DOI : 10.4153/CMB-1988-006-8
Mots-clés : H-closed, H-set, C-compact, seminormal, Primary 54D25 
Krystock, Robert L. ON H-Sets and Open Filter Adherences(1). Canadian mathematical bulletin, Tome 31 (1988) no. 1, pp. 37-44. doi: 10.4153/CMB-1988-006-8
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     title = {ON {H-Sets} and {Open} {Filter} {Adherences(1)}},
     journal = {Canadian mathematical bulletin},
     pages = {37--44},
     year = {1988},
     volume = {31},
     number = {1},
     doi = {10.4153/CMB-1988-006-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1988-006-8/}
}
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