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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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A function space $C_{p}(X)$ without a condensation onto a $\sigma$-compact space
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by Witold Marciszewski PDF
Proc. Amer. Math. Soc. 131 (2003), 1965-1969 Request permission

Abstract:

Assuming that the minimal cardinality of a dominating family in $\omega ^{\omega }$ is equal to $2^{\omega }$, we construct a subset $X$ of a real line $\mathbb {R}$ such that the space $C_{p}(X)$ of continuous real-valued functions on $X$ does not admit any continuous bijection onto a $\sigma$-compact space. This gives a consistent answer to a question of Arhangelā€™skii.
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Additional Information
  • Witold Marciszewski
  • Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
  • Address at time of publication: Faculty of Sciences, Division of Mathematics and Computer Science, Vrije Universiteit, De Boelelaan $1081^{{a}}$, 1081 HV Amsterdam, The Netherlands
  • MR Author ID: 119645
  • Email: wmarcisz@mimuw.edu.pl
  • Received by editor(s): July 2, 2001
  • Received by editor(s) in revised form: December 4, 2001, and February 8, 2002
  • Published electronically: October 18, 2002
  • Additional Notes: The author was supported in part by KBN grant 2 P03A 011 15.
  • Communicated by: Alan Dow
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 1965-1969
  • MSC (2000): Primary 54C35, 54A10
  • DOI: https://doi.org/10.1090/S0002-9939-02-06668-6
  • MathSciNet review: 1955287