Four-point characterizations of real inner product spaces

Autor:	Raymond W. Freese, Edward Z. Andalafte
Rok vydání:	2002
Předmět:	Euclidean distance Combinatorics Discrete mathematics Inner product space Metric space Eight-dimensional space Euclidean space Affine space Interpolation space Geometry and Topology Mathematics Convex metric space
Zdroj:	Journal of Geometry. 75:97-105
ISSN:	0047-2468
DOI:	10.1007/s00022-002-1386-z
Popis:	Generalized euclidean spaces have been characterized among metric spaces by the requirement that each member of certain classes of quadruples of points of the metric space be congruent to a quadruple of points of a euclidean space. The present paper strengthens earlier characterizations which only require the embedding of certain classes of quadruples which contain a linear triple and in which some three of the six distances between pairs of points are equal. These results generalize some similar characterizations of euclidean spaces among normed linear spaces.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ce6cf79a17474d58800fc4424f6e1819 https://doi.org/10.1007/s00022-002-1386-z Zobrazit plný text záznamu Full text from SpringerLink