Approximative properties of sets and continuous selectionsстатья
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Дата последнего поиска статьи во внешних источниках: 2 декабря 2020 г.
Аннотация: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.