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Characterization of Bounded Sets in Terms of Asymptotic Cones and Homotheties

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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.

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Funding

This work was supported by the 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).

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of Russian Academy of Sciences, Ekaterinburg, 620990, Russia

    A. V. Marinov

  2. Yeltsin Ural Federal University, Ekaterinburg, 620002, Russia

    A. V. Marinov

Authors
  1. A. V. Marinov
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Correspondence to A. V. Marinov.

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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 5, pp. 717–733.

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Marinov, A.V. Characterization of Bounded Sets in Terms of Asymptotic Cones and Homotheties. Math Notes 107, 791–803 (2020). https://doi.org/10.1134/S0001434620050077

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  • DOI: https://doi.org/10.1134/S0001434620050077

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