Nonnormal spaces $C_p(X)$ with countable extent
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- by Winfried Just, Ol’ga V. Sipacheva and Paul J. Szeptycki PDF
- Proc. Amer. Math. Soc. 124 (1996), 1227-1235 Request permission
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 $\diamondsuit$.References
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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
- MR Author ID: 246154
- Email: sipa@glas.apc.org
- Paul J. Szeptycki
- Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
- Email: szeptyck@ace.cs.ohiou.edu
- 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 - © Copyright 1996 American Mathematical Society
- 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