Abstract
In this paper we prove finiteness principles for \({C^m{({\mathbb{R}^n},{\mathbb{R}^D)}}}\) and \({C^{m-1,1}(\mathbb{R}^n,\mathbb{R}^D)}\) selections. In particular, we provide a proof for a conjecture of Brudnyi-Shvartsman (1994) on Lipschitz selections for the case when the domain is \({X=\mathbb{R}^n}\).
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Fefferman, C., Israel, A. & Luli, G.K. Finiteness Principles for Smooth Selection. Geom. Funct. Anal. 26, 422–477 (2016). https://doi.org/10.1007/s00039-016-0366-7
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DOI: https://doi.org/10.1007/s00039-016-0366-7