Abstract
The relations between the lower semicontinuity of the metric projection P G onto a finite-dimensional subspace G of L 1, the Lipschitz continuity of P G , the existence of continuous selections for P G , and uniform strong uniqueness of P G are studied. In particular, the lower semicontinuity of P G , the Lipschitz continuity of P G , and the uniform strong uniqueness of P G are all equivalent. If P G is lower semicontinuous, then P G has a Lipschitz continuous selection. Moreover, if G is one-dimensional, P G has a continuous selection if and only if it has a Lipschitz continuous selection.
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