2000/10/27 by Jesús Araujo, Jesus Araujo, Araujo, Jesus
Mathematics · #46E40 (Secondary) #54C35 (Primary) 54C40 #54D60 #Advanced Banach Space Theory #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #math.FA #math.GN #msc:46E40 #msc:54C35 #msc:54C40 #msc:54D60
paper · pdf · doi:10.48550/arxiv.math/0010261
15 pages, LaTeX. Results stated for arbitrary normed spaces without changes in proofs. New presentation and new examples. One reference added
openalex publication_date 2000/10/27 · arxiv created 2001/05/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.