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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Metric spaces in which minimal circuits cannot self-intersect
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by David Sanders PDF
Proc. Amer. Math. Soc. 56 (1976), 383-387 Request permission

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 $c$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 383-387
  • MSC: Primary 05C35; Secondary 54E35
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0414425-8
  • MathSciNet review: 0414425