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lf Vis a clused and nun-empty subset uf e. (7), the Banach space uf alí real-valued bounded functiuns un a set T, then existence uf best appruximants frum V and Lipschitz cuntinuity uf the metric projectiun in the Hausdorff metrie are pruved, whenever Vitas the fulluwinglattice uperatiun property: ((w+e)ísh)V(a>—e) belungs tu V, fur every a> and hin Vand e>O.

Best Approximants for Bounded Functions and the Lattice Operations