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

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

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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[1] 1. Berri, M., Porter, J., and Stephenson, R., A survey of minimal topological spaces, Proc. Kanpur Topology Conference, 1968, Academic Press, 1970, pp. 93–114. Google Scholar

[2] 2. Dickman, R. Jr. and Porter, J., Between minimal Hausdorff and compact Hausdorff spaces, Auburn Topology Conference, Spring Meeting, 1984. Google Scholar

[3] 3. Joseph, J., Multifunctions and cluster sets, Proc. Amer. Math. Soc. 74 (1979), pp. 329–337. Google Scholar

[4] 4. Porter, J. and Thomas, J., On H-closed and minimal Hausdorff spaces, Trans. Amer. Math. Soc. 138(1969), pp. 159–170. Google Scholar

[5] 5. Velicko, N., H-closed topological spaces, Mat. Sb. 70 (1966), pp. 98–112. Amer. Math. Soc. Transi. 78 (1968), pp. 103-118. Google Scholar

[6] 6. Vermeer, J., Closed subspaces of H-closed spaces, Pacific J. Math. 1 (1985), pp. 229–247. Google Scholar

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

[8] 8. Viglino, G., Seminormal and C-compact spaces, Duke J. Math. 38 (1971), pp. 57–61. Google Scholar

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