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Characterizing a circle with the double midset property. (English) Zbl 0317.52003

MSC:
52A05 Convex sets without dimension restrictions (aspects of convex geometry)
54E40 Special maps on metric spaces
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References:
[1] 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.
[2] -, Characterizations of metric spaces by the use of their midsets: One-spheres (Unpublished manuscript, 1-14).
[3] A. D. Berard Jr. and W. Nitka, A new definition of the circle by the use of bisectors, Fund. Math. 85 (1974), no. 1, 49 – 55. · Zbl 0281.53042
[4] Leonard M. Blumenthal, Theory and applications of distance geometry, Oxford, at the Clarendon Press, 1953. · Zbl 0050.38502
[5] L. D. Loveland and J. E. Valentine, Convex metric spaces with 0-dimensional midsets, Proc. Amer. Math. Soc. 37 (1973), 568 – 571. · Zbl 0252.52009
[6] L. D. Loveland and S. G. Wayment, Characterizing a curve with the double midset property, Amer. Math. Monthly 81 (1974), 1003 – 1006. · Zbl 0291.54042
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