Characterizing a circle with the double midset property
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- by L. D. Loveland and J. E. Valentine PDF
- Proc. Amer. Math. Soc. 53 (1975), 443-444 Request permission
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.References
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A. D. Berard, Jr., Characterizations of metric spaces by the use of their midsets: One-spheres, Notices Amer. Math. Soc. 19 (1972), A-198. Abstract #691-54-11.
—, Characterizations of metric spaces by the use of their midsets: One-spheres (Unpublished manuscript, 1-14).
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- Leonard M. Blumenthal, Theory and applications of distance geometry, Oxford, at the Clarendon Press, 1953. MR 0054981
- L. D. Loveland and J. E. Valentine, Convex metric spaces with $0$-dimensional midsets, Proc. Amer. Math. Soc. 37 (1973), 568–571. MR 310817, DOI 10.1090/S0002-9939-1973-0310817-3
- L. D. Loveland and S. G. Wayment, Characterizing a curve with the double midset property, Amer. Math. Monthly 81 (1974), 1003–1006. MR 418059, DOI 10.2307/2319308
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 443-444
- MSC: Primary 52A05; Secondary 54E40
- DOI: https://doi.org/10.1090/S0002-9939-1975-0388242-0
- MathSciNet review: 0388242