Blaschke selection theorem

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The Blaschke selection theorem is a result in topology and convex geometry about sequences of convex sets. Specifically, given a sequence of convex sets contained in a bounded set, the theorem guarantees the existence of a subsequence and a convex set such that converges to in the Hausdorff metric. The theorem is named for Wilhelm Blaschke.

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As an example of its use, the isoperimetric problem can be shown to have a solution.[1] That is, there exists a curve of fixed length that encloses the maximum area possible. Other problems likewise can be shown to have a solution:


  1. ^ a b c Paul J. Kelly; Max L. Weiss (1979). Geometry and Convexity: A Study in Mathematical Methods. Wiley. pp. Section 6.4.
  2. ^ Wetzel, John E. (July 2005). "The Classical Worm Problem --- A Status Report". Geombinatorics. 15 (1): 34–42.