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Proceedings of the American Mathematical Society

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Regular-closed, Urysohn-closed and completely Hausdorff-closed spaces.


Author: H. Herrlich
Journal: Proc. Amer. Math. Soc. 26 (1970), 695-698
MSC: Primary 54.22
DOI: https://doi.org/10.1090/S0002-9939-1970-0268838-2
MathSciNet review: 0268838
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Abstract: Recently M. P. Berri, J. R. Porter, and R. M. Stephenson, Jr. have given a survey on $ P$-closed and $ P$-minimal spaces. In the present paper the first two problems of this survey will be solved: (1) The product of two Urysohn-closed spaces need not be Urysohn-closed. (2) A completely Hausdorff-closed regular space need not be regular-closed.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0268838-2
Keywords: Urysohn-closed spaces, regular-closed spaces, completely Hausdorff-closed spaces, minimal topological spaces, products
Article copyright: © Copyright 1970 American Mathematical Society