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On condensations of $C_{p}$-spaces onto compacta

Author(s): A. V. Arhangel'skii
Journal: Proc. Amer. Math. Soc. 128 (2000), 1881-1883.
MSC (2000): Primary 54A10, 54C35, 54C10
Posted: February 25, 2000
Errata: Proc. Amer. Math. Soc. 130 (2002), 1875.
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Abstract: A condensation is a one-to-one onto mapping. It is established that, for each $\sigma $-compact metrizable space $X$, the space $C_{p}(X)$ of real-valued continuous functions on $X$ 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: 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
Posted: February 25, 2000
Communicated by: Alan Dow
Copyright of article: Copyright 2000, American Mathematical Society

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