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

Valentine, J. E.; Wayment, S. G.

doi:10.1090/S0002-9939-1975-0370375-6

Local Euclidean four-point properties which characterize inner-product spaces
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by J. E. Valentine and S. G. Wayment PDF

Proc. Amer. Math. Soc. 50 (1975), 337-343 Request permission

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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