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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Characterizing a circle with the double midset property


Authors: L. D. Loveland and J. E. Valentine
Journal: Proc. Amer. Math. Soc. 53 (1975), 443-444
MSC: Primary 52A05; Secondary 54E40
MathSciNet review: 0388242
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Abstract: A short and elementary proof is given to show that a space $ X$ is a circle with the natural geodesic metric if $ X$ is a nondegenerate, complete, convex metric space with the double midset property.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0388242-0
PII: S 0002-9939(1975)0388242-0
Keywords: Convex, midsets, bisectors, simple closed curves, double midset property
Article copyright: © Copyright 1975 American Mathematical Society