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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The regular continuous image of a minimal regular space is not necessarily minimal regular


Authors: Manuel P. Berriozabal and Carroll F. Blakemore
Journal: Proc. Amer. Math. Soc. 51 (1975), 453-454
MSC: Primary 54D25
DOI: https://doi.org/10.1090/S0002-9939-1975-0388340-1
MathSciNet review: 0388340
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Abstract: Herrlich has shown that the regular continuous image of a regular-closed space is regular-closed. In this paper, an example is given to show that Herrlich's result cannot be extended to a corresponding result for minimal regular spaces. Also, a modification of this example shows that a continuous function from a minimal regular space onto a regular space is not necessarily a closed function.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0388340-1
Keywords: Minimal regular spaces, regular-closed spaces, closed continuous functions
Article copyright: © Copyright 1975 American Mathematical Society