Geodesic
Constructing selections stepwise over skeletons of nerves of covers
Serdica Mathematical Journal, Tome 44 (2018) no. 1-2, pp. 137-154.

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It is given a simplified and self-contained proof of the classical Michael’s finite-dimensional selection theorem. The proof is based on approximate selections constructed stepwise over skeletons of nerves of covers. The method is also applied to simplify the proof of the Schepin–Brodsky’s generalisation of this theorem.
Keywords: Lower semi-continuous mapping, lower locally constant mapping, continuous selection, local connectedness in finite dimension, finite-dimensional space, 54C60, 54C65, 54F35, 54F45 
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     title = {Constructing selections stepwise over skeletons of nerves of covers},
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Gutev, Valentin. Constructing selections stepwise over skeletons of nerves of covers. Serdica Mathematical Journal, Tome 44 (2018) no. 1-2, pp. 137-154. http://geodesic.mathdoc.fr/item/SMJ2_2018_44_1-2_a6/