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Matematicheskie Zametki, 2020, Volume 107, Issue 5, Pages 717–733
DOI: https://doi.org/10.4213/mzm12393 (Mi mzm12393) 		 
Characterization of Bounded Sets in Terms of Asymptotic Cones and Homotheties

A. V. Marinovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Institute of Natural Sciences and Mathematics, Ural Federal University
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DOI: https://doi.org/10.4213/mzm12393
Abstract: A characterization of bounded sets in Banach spaces in terms of asymptotic cones and the Hausdorff deviations of sets from them homothetic images is obtained. Similar results for generalizations of the notion of boundedness are presented. Boundedness criteria have previously been known only for recessively compact sets.
Keywords: asymptotic cone, recession cone, homothety, bounded set, recessively compact set.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
This work was supported by Competitiveness Enhancement Program, Ural Federal University (Russian Federation Government order no. 211 of March 16, 2013, contract no. 02. A03.21.0006 of August 27, 2013).
Received: 28.03.2019
English version:
Mathematical Notes, 2020, Volume 107, Issue 5, Pages 791–803
DOI: https://doi.org/10.1134/S0001434620050077
Bibliographic databases:
Document Type: Article
UDC: 517.982.22
Language: Russian
Citation: A. V. Marinov, “Characterization of Bounded Sets in Terms of Asymptotic Cones and Homotheties”, Mat. Zametki, 107:5 (2020), 717–733; Math. Notes, 107:5 (2020), 791–803
Citation in format AMSBIB
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