A function space without a condensation onto a -compact space

Author:
Witold Marciszewski

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1965-1969

MSC (2000):
Primary 54C35, 54A10

Published electronically:
October 18, 2002

MathSciNet review:
1955287

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Abstract: Assuming that the minimal cardinality of a dominating family in is equal to , we construct a subset of a real line such that the space of continuous real-valued functions on does not admit any continuous bijection onto a -compact space. This gives a consistent answer to a question of Arhangel'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

Email:
wmarcisz@mimuw.edu.pl

DOI:
https://doi.org/10.1090/S0002-9939-02-06668-6

Keywords:
Function space,
pointwise convergence topology,
$C_{p}(X)$,
condensation

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

Article copyright:
© Copyright 2002
American Mathematical Society