Abstract:In a finite-dimensional Banach space, a closed set with lower semicontinuous metric projection is shown to have a continuous selection of the near-best approximation operator. Such a set is known to be a sun. In the converse question of the stability of best approximation by suns, it is proved that a strict sun in a finite-dimensional Banach space of dimension at most 3 is a P -sun, has a contractible set of nearest points, and admits a continuous ε-selection from the operator of near-best approximation for an… Show more
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