Properties of metrizable spaces X preserved by homeomorphisms of function spaces C_p(X)
by
Witold Marciszewski
Institute of Mathematics, University of Warsaw, Poland

For a completely regular space X, by C_p(X) we denote the space of continuous real valued functions on X, endowed with the pointwise convergence topology. When dealing with the problem of topological classification of function spaces C_p(X) one encounters the following general question: which topological properties of the space X are preserved by homeomorphisms of spaces C_p(X)? We will discuss some recent results of this kind concerning the case when X is a metrizable space.

We prove that, for metrizable spaces X and Y with homeomorphic function spaces C_p(X) and C_p(Y), X is countably dimensional if and only if Y is so. We also show that homeomorphisms of C_p(X) preserve absolute Borel classes greater than 2 and all projective classes of spaces X.

Date received: June 25, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeu-48.