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A Class of Spaces in Which Compact Sets are Finite

Published online by Cambridge University Press:  20 November 2018

P. L. Sharma*
Affiliation:
Department of Mathematics, University of Missour-RollaRolla, Missouri 65401, USA
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Abstract

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It is shown that in a dense-in-itself Hausdorff space if every set having a dense interior is open, then every compact set is finite.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Bankston, P., Topological reduced products via good ultrafilters, Gen. Top. and its Appl.. 10 (1979), 121-137.Google Scholar
2. Bankston, P., The total negation of a topological property, HI. Jour, of Math. 23 (1979), 241-252.Google Scholar
3. Bourbaki, N., General topology, Part I, Addison Wesley, Mass., 1966 Google Scholar
4. Hewitt, E., A problem in set theoretic topology, Duke Math. J.. 10 (1943), 309-333.Google Scholar
5. Kirch, M. R., A class of spaces in which compact sets are finite, Amer. Math. Monthly. 76 (1969), 42.Google Scholar
6. Levine, N., On the equivalence of compactness and finiteness in topology, Amer. Math. Monthly. 75 (1968), 178-180.Google Scholar