Characterization of Bounded Sets in Terms of Asymptotic Cones and Homotheties

A. V. Marinov<sup>ab

a</sup> 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.

UDC: 517.982.22

Received: 28.03.2019

DOI: 10.4213/mzm12393

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

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