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.
@article{arxiv.1809.07745,
title = {Constructing Selections Stepwise Over Skeletons of Nerves of Covers},
author = {Valentin Gutev},
journal= {arXiv preprint arXiv:1809.07745},
year = {2019}
}