Abstract
In this paper, authors de ne nearly dentability of Banach space. Authors prove that X is approxi- matively compact if and only if (1) X is nearly dentable space, and (2) X is nearly strict convex space. By the method of geometry of Banach spaces, authors also prove that if X is nearly dentable space, then for any closed convex subset C , metric projector PC is upper semicontinuous. Finally, authors give important application of nearly dentability in generalized inverse theory.
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