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Mat. Zametki, 2020, Volume 107, Issue 5, Pages 717–733 (Mi mz12393)  

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

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).


DOI: https://doi.org/10.4213/mzm12393

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English version:
Mathematical Notes, 2020, 107:5, 791–803

Bibliographic databases:

UDC: 517.982.22
Received: 28.03.2019

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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