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Journal of Convex Analysis 14 (2007), No. 1, 109--117
Copyright Heldermann Verlag 2007

Hausdorff Distance and Convex Sets

Michael D. Wills
Weber State University, Mathematics Department, 1702 University Circle, Ogden, UT 84408-1702, U.S.A.

If A and B are two bounded, closed, non-empty, and convex subsets of a normed space X, then the Hausdorff distance between A and B is the same as the Hausdorff distance between the boundary of A and the boundary of B.

Keywords: Hausdorff distance, convex sets.

MSC: 52A07

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