Realcompactness and Banach-Stone theorems
Abstract
Description
For realcompact spaces X and Y we give a complete description of the linear biseparating maps between spaces of vector-valued continuous functions on X and Y, where special attention is paid to spaces of vector-valued bounded continuous functions. These results are applied to describe the linear isometries between spaces of vector-valued bounded continuous and uniformly continuous functions.
14 pages, LaTeX, no figures. Changes in introduction. In section 2 results valid for normed spaces instead of Banach spaces
14 pages, LaTeX, no figures. Changes in introduction. In section 2 results valid for normed spaces instead of Banach spaces