Metric spaces in which minimal circuits cannot self-intersect
David Adrian Sanders · Proceedings of the American Mathematical Society · 1976
Definitions are given for self-intersecting polygons and cogeodesic points in terms of betweenness, and then it is proved that the metric spaces in which minimal polygons on a finite number of distinct noncogeodesic points are not self-intersecting are completely characterized as those metric spaces which have the following betweenness property for any four distinct points: if b b is between a a and c c and between a a and d d then either c c is between a a and d d or d d is between a a and c c .