Weak homogeneity of metric pythagorean orthogonality

Autor:	Raymond W. Freese, Edward Z. Andalafte
Rok vydání:	1996
Předmět:	Euclidean distance Metric space Pure mathematics Uniform continuity Euclidean space Injective metric space Mathematical analysis Geometry and Topology Equivalence of metrics Convex metric space Intrinsic metric Mathematics
Zdroj:	Journal of Geometry. 56:3-8
ISSN:	1420-8997 0047-2468
DOI:	10.1007/bf01222677
Popis:	It is known that euclidean or hyperbolic spaces are characterized among certain metric spaces by the property of linearity of the equidistant locus of pairs of points. In this paper, this linearity requirement is replaced by the requirement of convexity of the set of points which are metrically pythagorean orthogonal to a given segment at a given point. As a result a new characterization of real inner product spaces among complete, convex, externally convex metric spaces is obtained.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7b2fbb2af91d71e239cd86f2b6f5cf00 https://doi.org/10.1007/bf01222677 Zobrazit plný text záznamu Full text from SpringerLink