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A Minimal Regular Space that is Not Strongly Minimal Regular

Published online by Cambridge University Press:  20 November 2018

Dix H. Pettey
Dix H. Pettey*
Affiliation:
University of Missouri, Columbia, Missouri
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A regular T 1 space is said to be R-closed if there is no regular T 1 space in which it can be embedded as a nonclosed subspace. A regular T 1 space is said to be minimal regular if no regular T1 topology on the underlying set is strictly weaker than the given topology. It is known (see [1, Theorem 4, p. 455]) that every minimal regular space is R-closed. An R-closed space, however, need not be minimal regular [3, Example 2, p. 288].

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 4 , 01 August 1976 , pp. 875 - 878
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Berri, Manuel P. and Sorgenfrey, R. H., Minimal regular spaces, Proc. Amer. Math. Soc. 14 (1963), 454–458.Google Scholar
2. Dugundji, James, Topology (Allyn and Bacon, Boston, Mass., 1966).Google Scholar
3. Herrlich, Horst, Tv-Abgeschlossenheit und Tv-minimalitàt, Math. Z. 88 (1965), 285–294.Google Scholar
4. Scarborough, C. T. and Stone, A. H., Products of nearly compact spaces, Trans. Amer. Math. Soc. m (1966), 131–147.Google Scholar
5. Stephenson, R. M., Two R-closed spaces, Canad. J. Math. U (1972), 286–292.Google Scholar