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

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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

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