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Matematicheskie Zametki, 2020, Volume 108, Issue 3, Pages 323–333
DOI: https://doi.org/10.4213/mzm12725 (Mi mzm12725) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (666 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm12725
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-a
18-01-00333-а
This work was supported by the Russian Foundation for Basic Research under grants 19-01-00332-a and 18-01-00333-a.
Received: 18.03.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 3, Pages 309–317
DOI: https://doi.org/10.1134/S0001434620090011
Bibliographic databases:
Document Type: Article
UDC: 517.982.256+517.982.252
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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