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Proceedings of the American Mathematical Society

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

 

 

Not all semiregular Urysohn-closed spaces are Katětov-Urysohn


Author: Jack R. Porter
Journal: Proc. Amer. Math. Soc. 25 (1970), 518-520
MSC: Primary 54.20
DOI: https://doi.org/10.1090/S0002-9939-1970-0257955-9
MathSciNet review: 0257955
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Abstract: A topological space is said to be Urysohn if every pair of distinct points have disjoint closed neighborhoods. In this note we give an example of a first countable semiregular Urysohn space which is closed in every Urysohn space in which it can be embedded, and on which there exists neither a coarser minimal Urysohn topology nor a coarser minimal first countable Urysohn topology.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0257955-9
Keywords: Minimal topological spaces, minimal Urysohn spaces, Urysohn-closed spaces, Katětov-Urysohn spaces, Urysohn spaces, separation axioms
Article copyright: © Copyright 1970 American Mathematical Society