Vol. 43, No. 1, 1972

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ISSN: 0030-8730
Criteria for Banach spaces

Joseph Earl Valentine and Stanley G. Wayment

Vol. 43 (1972), No. 1, 251–252
Abstract

It is well known in euclidean geometry that the quadrilateral obtained from an arbitrary quadrilateral by joining its midpoints is a parallelogram. The purpose of this paper is to show that a complete metric space with a unique metric line joining any pair of its distinct points is a Banach space if and only if it has the above mentioned property.

Mathematical Subject Classification 2000
Primary: 46B10
Milestones
Received: 16 August 1971
Published: 1 October 1972
Authors
Joseph Earl Valentine
Stanley G. Wayment