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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
Published electronically:
February 25, 2000
Erratum:
Proc. Amer. Math. Soc. 130 (2002), 1875.
MathSciNet review:
1751998
Full-text PDF Free Access
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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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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:
http://dx.doi.org/10.1090/S0002-9939-00-05758-0
PII:
S 0002-9939(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
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