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Continuous Selections for Continuous Set-Valued Mappings and Finite-Dimensional Sets

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Abstract

The paper is devoted to selection theorems for ‘continuous’ set-valued mappings which are not necessarily convex-valued on finite-dimensional subsets of the domain. As a result, we get natural generalizations of the famous Kuratowski–Dugundji extension theorem. The technique, developed in the paper, applies to l.s.c. mappings with paracompact, or similar, domain as well. Also, it leads us to a new construction of set-valued continuous selections that involves dimension-type arguments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ehime University, Matsuyama, 790, Japan

    Valentin G. Gutev

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  1. Valentin G. Gutev
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Gutev, V.G. Continuous Selections for Continuous Set-Valued Mappings and Finite-Dimensional Sets. Set-Valued Analysis 6, 149–170 (1998). https://doi.org/10.1023/A:1008649305964

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