On condensations of $C_{p}$-spaces onto compacta
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- by A. V. Arhangel’skii PDF
- Proc. Amer. Math. Soc. 128 (2000), 1881-1883 Request permission
Erratum: Proc. Amer. Math. Soc. 130 (2002), 1875-1875.
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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1751998