Geodesic
Continuous $\varepsilon$-selection
Sbornik. Mathematics, Tome 207 (2016) no. 2, pp. 267-285

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is concerned with properties of sets admitting a continuous selection from the set of nearly best approximations. Necessary and sufficient conditions are put forward for the existence of continuous additive and multiplicative $\varepsilon$-selections on closed sets. Sufficient conditions are given for the existence of continuous selections for stable set-valued mappings with not-necessarily-convex values. Bibliography: 8 titles.
Keywords: continuous selection, infinitely connected set, set-valued mapping. 
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     author = {I. G. Tsar'kov},
     title = {Continuous $\varepsilon$-selection},
     journal = {Sbornik. Mathematics},
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     volume = {207},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_2_a4/}
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I. G. Tsar'kov. Continuous $\varepsilon$-selection. Sbornik. Mathematics, Tome 207 (2016) no. 2, pp. 267-285. http://geodesic.mathdoc.fr/item/SM_2016_207_2_a4/