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 Arhangelāskii.References
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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