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
DOI:
https://doi.org/10.1090/S0002-9939-02-06668-6
Published electronically:
October 18, 2002
MathSciNet review:
1955287
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Abstract | References | Similar Articles | Additional Information
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