Metric Geometry in Normed Spaces
Identifieur interne : 000195 ( Istex/Curation ); précédent : 000194; suivant : 000196Metric Geometry in Normed Spaces
Auteurs : Mahlon M. Day [États-Unis]Source :
- Ergebnisse der Mathematik und ihrer Grenzgebiete ; 1973.
Abstract
Abstract: Banach’s book, p. 160, gives a theorem of Mazur and Ulam that an isometry of one normed space onto another which carries 0 to 0 is linear. This is true only for real-linear spaces, and is proved by characterizing the midpoint of a segment in a normed space in terms of the distance function. Using the same proof a slightly stronger result can be attained.
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DOI: 10.1007/978-3-662-09000-8_7
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