Not all semiregular Urysohn-closed spaces are Katětov-Urysohn

Porter, Jack R.

doi:10.1090/S0002-9939-1970-0257955-9

Not all semiregular Urysohn-closed spaces are Katětov-Urysohn
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by Jack R. Porter

Proc. Amer. Math. Soc. 25 (1970), 518-520

DOI: https://doi.org/10.1090/S0002-9939-1970-0257955-9

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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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