On condensations of 
-spaces onto compacta
Author:
A. V. Arhangel'skii
Journal:
Proc. Amer. Math. Soc. 128 (2000), 1881-1883
MSC (2000):
Primary 54A10, 54C35, 54C10
DOI:
https://doi.org/10.1090/S0002-9939-00-05758-0
Published electronically:
February 25, 2000
Erratum:
Proc. Amer. Math. Soc. 130 (2002), 1875.
MathSciNet review:
1751998
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Abstract | References | Similar Articles | Additional Information
Abstract: A condensation is a one-to-one onto mapping. It is established that, for each 
-compact metrizable space 
, the space 
of real-valued continuous functions on 
in the topology of pointwise convergence condenses onto a metrizable compactum. Note that not every Tychonoff space condenses onto a compactum.
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A.V. Arhangelskii,
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- [3] A.V. Arhangelskii, Function spaces in the topology of pointwise convergence and compact sets, Russian Math. Surveys 39:5 (1984), 9-56.
- [4] A.V. Arhangelskii and V.I. Ponomarev, Fundamentals of General Topology: Problems and Exercises, Reidel, 1984. MR 87i:54001
- [5] S. Banach, Livre Ecossais, Problem 1, 17:8, 1935; Colloq. Math. 1 (1947), p. 150.
- [6] T. Dobrowolski and W. Marciszewski, Classification of function spaces with the topology determined by a countable dense set, Fundamenta Mathematicae 148 (1995), 35-62. MR 96k:54017
- [7] E.G. Pytkeev, Upper bounds of Topologies, Matem. Notes 20:4 (1976), 831-837. MR 55:1262
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Additional Information
A. V. Arhangel'skii
Affiliation:
Department of Mathematics, 321 Morton Hall, Ohio University, Athens, Ohio 45701;
Chair of General Topology and Geometry, Mech.-Math. Faculty, Moscow State University, Moscow 119899, Russia
Email:
arhangel@bing.math.ohiou.edu, arhala@arhala.mccme.ru
DOI:
https://doi.org/10.1090/S0002-9939-00-05758-0
Keywords:
Condensation,
compactum,
network,
topology of pointwise convergence,
$\sigma $-compact space,
Borel space,
$P$-space
Received by editor(s):
May 24, 1997
Received by editor(s) in revised form:
May 15, 1998
Published electronically:
February 25, 2000
Communicated by:
Alan Dow
Article copyright:
© Copyright 2000
American Mathematical Society
