Abstract
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.
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Andalafte, E., Freese, R. Weak homogeneity of metric pythagorean orthogonality. J Geom 56, 3–8 (1996). https://doi.org/10.1007/BF01222677
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DOI: https://doi.org/10.1007/BF01222677