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 ##IMG## [http://ej.iop.org/images/1064-5616/211/8/1190/MSB_211_8_1190ieqn1.gif] {$V$} are employed to establish the existence of continuous selections of the relative (with respect to ##IMG## [http://ej.iop.org/images/1064-5616/211/8/1190/MSB_211_8_1190ieqn1.gif] {$V$} ) Chebyshev near-centre map and of the sets of relative (with respect to ##IMG## [http://ej.iop.org/images/1064-5616/211/8/1190/MSB_211_8_1190ieqn1.gif] {$V$} ) near-Ch...

中文翻译：

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集和连续选择的近似性质

研究了允许连续选择最佳和近似最佳算子的集合。Michael的经典连续选择定理扩展到有限维空间中的下半连续度量投影的情况（其值没有先验凸度条件）。在有限维多面体空间中提出了度量投影的充分条件，暗示了相应集合的日照度。太阳的可用结果## IMG ## [http://ej.iop.org/images/1064-5616/211/8/1190/MSB_211_8_1190ieqn1.gif] {$ V $}用于建立连续选择的存在亲戚（相对于## IMG ## [http://ej.iop.org/images/1064-5616/211/8/1190/MSB_211_8_1190ieqn1.gif] {$ V $}）切比雪夫近中心地图和相对的集合（相对于## IMG ## [http：//ej.iop。