Realcompactness and spaces of vector-valued functions
Abstract
Description
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.
15 pages, LaTeX. Results stated for arbitrary normed spaces without changes in proofs. New presentation and new examples. One reference added
15 pages, LaTeX. Results stated for arbitrary normed spaces without changes in proofs. New presentation and new examples. One reference added