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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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 $\diamondsuit$.
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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