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 Mat. Zametki, 2020, Volume 108, Issue 3, Pages 323–333 (Mi mz12725)

Characterization of Sets with Continuous Metric Projection in the Space $\ell^\infty_n$

A. R. Alimovabc

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
c Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We characterize the subsets of the space $\ell^\infty_n$ with continuous (lower semicontinuous) metric projection. One of the characteristic properties is the strict solarity of both the set and any nonempty intersection thereof with any support coordinate hyperplane.

Keywords: strict sun, continuity of metric projection, lower semicontinuity of metric projection, strictly monotone path-connected set.

 Funding Agency Grant Number Russian Foundation for Basic Research 19-01-00332-a18-01-00333-à This work was supported by the Russian Foundation for Basic Research under grants 19-01-00332-a and 18-01-00333-a.

DOI: https://doi.org/10.4213/mzm12725

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English version:
Mathematical Notes, 2020, 108:3, 309–317

Bibliographic databases:

UDC: 517.982.256+517.982.252

Citation: A. R. Alimov, “Characterization of Sets with Continuous Metric Projection in the Space $\ell^\infty_n$”, Mat. Zametki, 108:3 (2020), 323–333; Math. Notes, 108:3 (2020), 309–317

Citation in format AMSBIB
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