Minimal extremal subsets of the unit sphere

Best approximative properties of exposed faces of $l_1$

“…It is easily verified that ball proximinality implies proximinality. [1] Best approximative properties of hyperplanes or subspaces in general, of Banach spaces are closely related to structure of the unit ball and its exposed faces and study of geometric structure of the unit ball in view of this link, is not new [2]. We also refer to [3], [4], [5], [7] and Proposition 1 of [10] in this regard.…”

Closures of faces of compact convex sets

“…-The use of the Baire Category Theorem above was suggested by the proof of a similar result in [5]. The argument proving (1) => (2) could also be used here.…”

Simultaneous approximation and interpolation inL1andC(T)

“…In a recent paper of Deutsch and Lindahl [2], they showed that in certain spaces that the set Q(x), the intersection of all U(X) supporting hyperplanes at x, is equal to the closure of the minimal extremal subset containing ACKNOWLEDGMENT.…”