A characterization of regularity in topology
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- by Oswald Wyler PDF
- Proc. Amer. Math. Soc. 29 (1971), 588-590 Request permission
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.References
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C. Berge, Topological spaces, Macmillan, New York, 1963.
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- Ernest Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–182. MR 42109, DOI 10.1090/S0002-9947-1951-0042109-4
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 588-590
- MSC: Primary 54.23
- DOI: https://doi.org/10.1090/S0002-9939-1971-0281146-X
- MathSciNet review: 0281146