On angles in certain metric spaces

W. A. Wilson
1932 Bulletin of the American Mathematical Society  
1. Introduction. In a series of articles on metrical geometry f Menger has made a study of the geometry of certain abstract metric spaces and in particular he has obtained conditions for the congruence of metric spaces with sub-sets of euclidean spaces. In a recent article^ he suggests a system of axioms for "angle spaces" and related problems. It will be shown in this note that a theory of angles analogous to that of euclidean space is possible for convex complete metric spaces any four points
more » ... of which are congruent with four points in some euclidean space. From this certain theorems regarding tangents to simple arcs are deduced.
doi:10.1090/s0002-9904-1932-05463-5 fatcat:jzk7hneognchrom4weimjtu4ze