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The Transitive Property of Parallel Lines is a Characteristic Property of Real Strictly Convex Banach Spaces

1985
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Proceedings of the American Mathematical Society
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In a recent paper Freese and Murphy said a complete, convex, externally convex metric space has the vertical angle property provided for each four of its distinct points p, q, r, s, if m is a midpoint of p and q and of r and s. then pr = qs. In this paper we say a line L is parallel to a line N in such a space provided L and N contain points p, r, and q, s, respectively, such that the segments S(p,q) and S(r, s) have a common midpoint m. We further assume that if line L is parallel to line ¿V

doi:10.2307/2045851
fatcat:xuixg6wjcrayhaydvuudoe7r2m