On extension of isometries in (F)-spaces |
| |
Authors: | Ding Guanggui Huang Senzhong |
| |
Institution: | (1) Department of Mathematics, Nankai University, 300071 Tianjin, China;(2) Department of Mathematics, University of Iowa, 52242 Iowa City, IA, USA;(3) Mathematisehes Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany |
| |
Abstract: | An (F)-spaceE is said to be locally midpoint constricted (in short, Imp-constricted) if there exists some>0 such thatD(A/2) <D(A) for every subsetA ofE with 0<D(A), whereD(A) denotes the diameter ofA. Our main result goes as follow: LetE be an Imp-constricted (F)-space andU an open connected subset ofE. Assume thatT:U F is an isometry (i.e., a distance-preserving map) which mapsU onto an open subset of the (F)-spaceF. ThenT can be extended to an affine homeomorphism fromE toF. Also, some other results about the question whether each isometry between two (F)-spaces is affine are obtained. |
| |
Keywords: | Locally midpoint constricted Isometry Affine homeomorphism |
本文献已被 SpringerLink 等数据库收录! |
|