Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-14T12:23:18.937Z Has data issue: false hasContentIssue false
  • English
  • Français

ON H-Sets and Open Filter Adherences(1)

Published online by Cambridge University Press:  20 November 2018

Robert L. Krystock
Robert L. Krystock*
Affiliation:
Department of Mathematics and Statistics Mississippi State University, P.O. Drawer MA Mississippi State, MS 39762
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

H-closedH-setC-compactseminormalPrimary 54D25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 37 - 44
Copyright
Copyright © Canadian Mathematical Society 1988

Footnotes

(1)

The author's research was partially supported by the Research Initiation Program at Mississippi State University.

References

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. Dickman, R. Jr. and Porter, J., Between minimal Hausdorff and compact Hausdorff spaces, Auburn Topology Conference, Spring Meeting, 1984.Google Scholar
3. Joseph, J., Multifunctions and cluster sets, Proc. Amer. Math. Soc. 74 (1979), pp. 329–337.Google Scholar
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. 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. Vermeer, J., Closed subspaces of H-closed spaces, Pacific J. Math. 1 (1985), pp. 229–247.Google Scholar
7. Viglino, G., C-compact spaces, Duke J. Math. 36 (1969), pp. 761–764.Google Scholar
8. Viglino, G., Seminormal and C-compact spaces, Duke J. Math. 38 (1971), pp. 57–61.Google Scholar