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Weak continuity of metric projections

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Abstract

A necessary and sufficient condition is found for weak continuity of a metric projection onto a finite-dimensional subspace inl p (1<p≠2). A metric projection onto a boundedly compact set inl p is sequentially weakly upper semicontinueus. An example is given on a convex, compact set inl 2 onto which the metric projection is not weakly continuous.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Urals Scientific Center, Academy of Sciences of the USSR, USSR

    V. S. Balaganskii

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  1. V. S. Balaganskii
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Translated from Matematicheskie Zametki, Vol. 22, No. 3, pp. 345–356, September, 1977.

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Balaganskii, V.S. Weak continuity of metric projections. Mathematical Notes of the Academy of Sciences of the USSR 22, 681–687 (1977). https://doi.org/10.1007/BF02412495

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  • DOI: https://doi.org/10.1007/BF02412495

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