Geodesic
Characterization of Bounded Sets in Terms of Asymptotic Cones and Homotheties
Matematičeskie zametki, Tome 107 (2020) no. 5, pp. 717-733

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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. 
@article{MZM_2020_107_5_a4,
     author = {A. V. Marinov},
     title = {Characterization of {Bounded} {Sets} in {Terms} of {Asymptotic} {Cones} and {Homotheties}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {717--733},
     publisher = {mathdoc},
     volume = {107},
     number = {5},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_5_a4/}
}
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A. V. Marinov. Characterization of Bounded Sets in Terms of Asymptotic Cones and Homotheties. Matematičeskie zametki, Tome 107 (2020) no. 5, pp. 717-733. http://geodesic.mathdoc.fr/item/MZM_2020_107_5_a4/