Approximative properties of sets and continuous selections
Sbornik. Mathematics, Tome 211 (2020) no. 8, pp. 1190-1211
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Sets admitting a continuous selection of the operators of best and near-best approximation are studied. Michael's classical continuous selection theorem is extended to the case of a lower semicontinuous metric projection in finite-dimensional spaces (with no a priori convexity conditions on its values). Sufficient conditions on the metric projection implying the solarity of the corresponding set are put forward in finite-dimensional polyhedral spaces. Available results for suns $V$ are employed to establish the existence of continuous selections of the relative (with respect to $V$) Chebyshev near-centre map and of the sets of relative (with respect to $V$) near-Chebyshev points in certain classical spaces.
Bibliography: 30 titles.
Keywords:
set-valued mapping, continuous selection, sun, monotone path-connected set, relative Chebyshev centre and point.
@article{SM_2020_211_8_a5,
author = {I. G. Tsar'kov},
title = {Approximative properties of sets and continuous selections},
journal = {Sbornik. Mathematics},
pages = {1190--1211},
publisher = {mathdoc},
volume = {211},
number = {8},
year = {2020},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2020_211_8_a5/}
}
I. G. Tsar'kov. Approximative properties of sets and continuous selections. Sbornik. Mathematics, Tome 211 (2020) no. 8, pp. 1190-1211. http://geodesic.mathdoc.fr/item/SM_2020_211_8_a5/