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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 T1 space is said to be R-closed if there is no regular T1 space in which it can be embedded as a nonclosed subspace. A regular T1 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].

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

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