Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Metric spaces in which minimal circuits cannot self-intersect

Author: David Sanders
Journal: Proc. Amer. Math. Soc. 56 (1976), 383-387
MSC: Primary 05C35; Secondary 54E35
MathSciNet review: 0414425
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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 $b$ is between $a$ and $c$ and between $a$ and $d$ then either $c$ is between $a$ and $d$ or $d$ is between $a$ and $c$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05C35, 54E35

Retrieve articles in all journals with MSC: 05C35, 54E35

Additional Information

Keywords: Non-self-intersecting polygon, noncogeodesic points, geodesic metric space
Article copyright: © Copyright 1976 American Mathematical Society