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On the size of the set of points where the metric projection exists

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Abstract

In this paper we answer in the negative a question due to J. P. R. Christensen about almost everywhere existence of nearest points using a decomposition of ℓ2 due to J. Matoušek and E. Matoušková. We also formulate a similar question about almost everywhere existence of farthest points and answer it in the negative.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Jakub Duda

  2. Department of Mathematics, University of Missouri, 202 Math Sciences Building, 65211-4100, Columbia, MO, USA

    Jakub Duda

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  1. Jakub Duda
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The author was supported by the grant GAČR 201/00/0767 (from the Grant Agency of the Czech Republic).

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Duda, J. On the size of the set of points where the metric projection exists. Isr. J. Math. 140, 271–283 (2004). https://doi.org/10.1007/BF02786636

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  • DOI: https://doi.org/10.1007/BF02786636

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