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Monotone and Čebyšev arcs in hyperspaces

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An Erratum to this article was published on 01 August 2010

Abstract

A set in a metric space is called a Čebyšev set if it contains a unique “nearest neighbour” to each point of the space. In this paper we introduce the concept of a monotone arc of convex sets and show that compact monotone arcs have the Čebyšev property in the hyperspace of compact strictly convex sets. In the hyperspace of compact convex sets only certain monotone arcs are Čebyšev ; these are characterized. Results are also obtained for affine segments and for noncompact monotone arcs.

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Correspondence to Robert J. MacG. Dawson.

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Funded by a NSERC Discovery grant.

An erratum to this article can be found at http://dx.doi.org/10.1007/s00022-010-0050-2

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Dawson, R.J.M. Monotone and Čebyšev arcs in hyperspaces. J. Geom. 98, 1–19 (2010). https://doi.org/10.1007/s00022-010-0044-0

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  • DOI: https://doi.org/10.1007/s00022-010-0044-0

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