Abstract
By presenting counterexamples and a new proof, we determine all metric vector spaces, for which the theorem of ALEXANDROFF-LESTER holds. In this context, the theorem will be extended to certain nonregular metric vector spaces of characteristic 2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literatur
Alexandroff, A.D.: Seminar report. Uspehi Mat. Nauk. 5 (1950), no. 3 (37), 187.
Borchers, H.J., Hegerfeldt, G.C.: The structure of space-time transformations. Commun. Math. Phy. 28 (1972), 259–266.
Buekenhout, F.: Ensembles quadratiques des espaces projectifs. Math. Z. 110 (1969), 306–318.
Lenz, H.: Bemerkungen zum Beckman-Quarles-Problem. Erscheint in Mitt. d. Math. Ges. in Hamburg.
Lester, J.A.: Cone preserving mappings for quadratic cones over arbitrary fields. Can. J. Math. 29 (1977), 1247–1253.
Scharlau, W.: Quadratic and Hermitian Forms. Berlin 1985.
Schröder, E.M.: Zur Kennzeichnung distanztreuer Abbildungen in nichteuklidischen Räumen. J. Geometry 15 (1980), 108–118.
Schröder, E.M.: Fundamentalsätze der metrischen Geometrie. J. Geometry 27 (1986), 36–59.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Giuseppe Tallini on the occasion of his 60th birthday
Herrn H. Lenz danke ich für mehrere Vorschläge zur durchsichtigeren Formulierung der Beweise.
Rights and permissions
About this article
Cite this article
Schröder, E.M. Ein einfacher Beweis des Satzes von Alexandroff-Lester. J Geom 37, 153–158 (1990). https://doi.org/10.1007/BF01230368
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01230368