Best Approximants for Bounded Functions and the Lattice Operations
If is a closed and non-empty subset of , the Banach space of all real-valued bounded functions on a set , then existence of best approximants from and Lipschitz continuity of the metric projection in the Hausdorff metric are proved, whenever has the following lattice operation property: belongs to , for every and in and .
1991 Mathematics Subject Classification: 41A65, 41A50, 46E05.