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Nonnormal spaces $C_{p}(X)$ with countable extent


Authors: Winfried Just, Ol'ga V. Sipacheva and Paul J. Szeptycki
Journal: Proc. Amer. Math. Soc. 124 (1996), 1227-1235
MSC (1991): Primary 03E75, 54A20, 54A35, 54C35, 54G20
DOI: https://doi.org/10.1090/S0002-9939-96-03500-9
MathSciNet review: 1343704
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Abstract: Examples of spaces $X$ are constructed for which $C_{p}(X)$ is not normal but all closed discrete subsets are countable. A monolithic example is constructed in ZFC and a separable first countable example is constructed using $\diamondsuit$.


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Additional Information

Winfried Just
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
Email: just@ace.cs.ohiou.edu

Ol'ga V. Sipacheva
Affiliation: Chair of General Topology and Geometry, Mechanics and Mathematics Faculty, Moscow State University, 119899 Moscow, Russia
Email: sipa@glas.apc.org

Paul J. Szeptycki
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
Email: szeptyck@ace.cs.ohiou.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03500-9
Keywords: $C_{p}(X)$, extent, normality, $\diamondsuit$, almost disjoint family, $\Psi$-space, p-ultrafilter, Luzin gap
Received by editor(s): April 6, 1994
Additional Notes: The first author was partially supported by NSF grant DMS-9312363
The second author collaborated while visiting Ohio University
Article copyright: © Copyright 1996 American Mathematical Society

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