Criteria for Banach spaces

Joseph Valentine, Stanley Wayment
1972 Pacific Journal of Mathematics  
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.
doi:10.2140/pjm.1972.43.251 fatcat:tzoqmxa765e53d46v24toe2xe4