A normal first countable ccc nonseparable space
Author:
Murray G. Bell
Journal:
Proc. Amer. Math. Soc. 74 (1979), 151155
MSC:
Primary 54D15; Secondary 54G20
MathSciNet review:
521889
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Abstract: We construct an absolute example of a space having the properties in the title. Let Y be the set of nonempty finite subsets of the Cantor cube of countable weight. The PixleyRoy topology on Y is not normal, but the Vietoris topology on Y is normal. Our space can be considered a normalization of the PixleyRoy topology on Y by adding cluster points which as a subspace have the Vietoris topology. The Alexandroff duplicating procedure is used liberally to glue the space together. The example is also a sigma compact paracompact pspace. If further settheoretic assumptions are made (e.g. or ), then it is known that even perfectly normal such examples exist.
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 , Density of compactifications, SetTheoretic Topology, ed. G. M. Reed, Academic Press, New York, 1977. MR 0431077 (55:4079)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197905218890
PII:
S 00029939(1979)05218890
Keywords:
First countable,
normal,
ccc,
separable
Article copyright:
© Copyright 1979
American Mathematical Society
