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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Keywords:
Minimal topological spaces,
minimal Urysohn spaces,
Urysohn-closed spaces,
Katětov-Urysohn spaces,
Urysohn spaces,
separation axioms
Article copyright:
© Copyright 1970
American Mathematical Society