On the size of the set of points where the metric projection exists |
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| Authors: | Jakub Duda |
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| Institution: | (1) Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic;(2) Department of Mathematics, University of Missouri, 202 Math Sciences Building, 65211-4100 Columbia, MO, USA |
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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.
The author was supported by the grant GAČR 201/00/0767 (from the Grant Agency of the Czech Republic). |
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