2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60237For 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 spacesFunctional AnalysisGeneral Topology46E40 (Primary) 47B33, 47B38, 54D60 (Secondary)text