Realcompactness and spaces of vector-valued functions
| dc.creator | Araujo, Jesus | |
| dc.date | 2000-10-27 | |
| dc.date | 2001-05-14 | |
| dc.date.accessioned | 2026-07-07T04:38:16Z | |
| dc.date.available | 2026-07-07T04:38:16Z | |
| dc.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. | |
| dc.description | 15 pages, LaTeX. Results stated for arbitrary normed spaces without changes in proofs. New presentation and new examples. One reference added | |
| dc.identifier | https://arxiv.org/abs/math/0010261 | |
| dc.identifier | http://arxiv.org/abs/math/0010261 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60213 | |
| dc.subject | General Topology | |
| dc.subject | Functional Analysis | |
| dc.subject | 54C35 (Primary) 54C40, 54D60, 46E40 (Secondary) | |
| dc.title | Realcompactness and spaces of vector-valued functions | |
| dc.type | text |