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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On regular-invariance of continuity


Authors: R. G. Ori and M. Rajagopalan
Journal: Proc. Amer. Math. Soc. 88 (1983), 725-726
MSC: Primary 54A10; Secondary 54C05
MathSciNet review: 702308
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Abstract: Let $ (X,\sigma )$ be a given topological space. A compression $ \tau $ of $ \sigma $ is regular-invariant if and only if for every regular space $ Y$ the $ \sigma $-continuous functions into $ Y$ are also $ \tau $-continuous. $ \sigma $ is regular minimal if no proper compression of $ \sigma $ is regular-invariant. J. A. Guthrie and H. E. Stone posed the problem of whether every semiregular space is regular minimal. We answer this question in the negative.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0702308-9
PII: S 0002-9939(1983)0702308-9
Article copyright: © Copyright 1983 American Mathematical Society