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On properties of metrizable spaces X preserved by t-equivalence

Part of: Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  26 February 2010

Witold Marciszewski
Witold Marciszewski
Affiliation:
Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland. E-mail: wmarcisz@mimuw.edu.pl
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Abstract

For a completely regular space X, denote by Cp(X) the space of continuous real valued functions on X, endowed with the pointwise convergence topology. The spaces X and Y are t-equivalent if Cp(X) and Cp(Y) are homeomorphic. It is proved that, for metrizable spaces X, the countable dimensionality is preserved by t-equivalence. It is also shown that this relation preserves absolute Borel classes greater than 2 and all projective classes.

MSC classification

Secondary: 54C35: Function spaces
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 273 - 279
Copyright
Copyright © University College London 2000

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