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

A characterization of regularity in topology


Author: Oswald Wyler
Journal: Proc. Amer. Math. Soc. 29 (1971), 588-590
MSC: Primary 54.23
MathSciNet review: 0281146
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Abstract: We show in this paper that a topological space satisfies $ {T_3}$ (which we do not intend to imply $ {T_2}$) if and only if convergence of filters is a continuous relation. In particular, a Hausdorff space is regular if and only if convergence of filters is a continuous mapping. We propose a new, categorically motivated, definition of continuous relations between topological spaces, and we compare it with two existing continuity concepts for relations.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0281146-X
PII: S 0002-9939(1971)0281146-X
Keywords: Regular topological space, regular Hausdorff space, convergence of filters, continuous relation, upper semicontinuous relation, lower semicontinuous relation
Article copyright: © Copyright 1971 American Mathematical Society