Finite Dimensional Chebyshev Subspaces of l∞

If A is a subset of the normed linear space X, then A is said to be proximinal in X if for each xƐX there is a point y0ƐA such that the distance between x and A; d(x, A) = inf{||xy||: yƐA}= ||x-y0||. The element y0 is called a best approximation for x from A. If for each xƐX, the best approximation for x from A is unique then the subset A is called a Chebyshev subset of X. In this paper the author studies the existence of finite dimensional Chebyshev subspaces of l∞.