Realcompactness and spaces of vector-valued functions
Abstract
It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y; in particular we find remarkable differences with respect to the scalar context: namely, if E and F are infinite-dimensional and T is a biseparating map between the space of E-valued bounded continuous functions on X and that of F-valued bounded continuous functions on Y, then the realcompactifications of X and Y are homeomorphic.
Cite
@article{arxiv.math/0010261,
title = {Realcompactness and spaces of vector-valued functions},
author = {Jesus Araujo},
journal= {arXiv preprint arXiv:math/0010261},
year = {2007}
}
Comments
15 pages, LaTeX. Results stated for arbitrary normed spaces without changes in proofs. New presentation and new examples. One reference added