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Local Euclidean four-point properties which characterize inner-product spaces

Authors: J. E. Valentine and S. G. Wayment
Journal: Proc. Amer. Math. Soc. 50 (1975), 337-343
MSC: Primary 52A50; Secondary 46C05
MathSciNet review: 0370375
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Abstract: Let $ M$ be a complete, convex, externally convex metric space. We show $ M$ is an inner-product space if and only if for each point $ t$ of $ M,M$ contains a sphere $ {S_t}$ which has the euclidean queasy, feeble or weak four-point property.

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Keywords: Banach space, complete, convex, externally convex, inner-product space, local euclidean four-point properties, metric space
Article copyright: © Copyright 1975 American Mathematical Society

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