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Characterizations of s-closed Hausdorff spaces

Published online by Cambridge University Press:  09 April 2009

Takashi Noiri
Affiliation:
Yatsushiro Collegeof TechnologyYatsushiro Kumamoto 866, Japan
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A topological space X is said to be S-closed if every cover of X by regular closed sets of X has a finite subcover. In this note some characterizations of S-closed Hausdorff spaces are obtained.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Crossley, S. Gene and Hildebrand, S. K., ‘Semi-closure’, Texas J. Sci. 22 (1971), 99112.Google Scholar
[2]Di Maio, G., ‘S-closed spaces, S-sets and S-continuous functions’, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 118 (1984), 125134.Google Scholar
[3]Ganster, M., Noiri, T. and Reilly, I. L., ‘Weak and strong forms of θ-irresolute functions’, J. Inst. Math. Comp. Sci. Math. Ser. 1 (1988), 1929.Google Scholar
[4]Herrmann, R. A., ‘RC-convergence’, Proc. Amer. Math. Soc. 75 (1979), 311317.CrossRefGoogle Scholar
[5]Joseph, J. E. and Kwack, M. H., ‘On S-closed spaces’, Proc. Amer. Math. Soc. 80 (1980), 341348.Google Scholar
[6]Levine, N., ‘Semi-open sets and semi-continuity in topological spaces’, Amer. Math. Monthly 70 (1963), 3641.CrossRefGoogle Scholar
[7]Noiri, T., ‘On S-closed subspaces’, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fi. Mat. Natur. (8) 64 (1978), 157162.Google Scholar
[8]Soundararajan, T., ‘Weakly Hausdorff spaces and the cardinality of topological spaces’, General Topology and its Relations to Modern Analysis and Algebra III, Proc. Conf. Kampur, 1968; pp. 301306 (Academia, Prague, 1971).Google Scholar
[9]Thompson, T., ‘S-closed spaces’, Proc. Amer. Math. Soc. 60 (1976), 335338.Google Scholar