Super weak compactness and uniform Eberlein compacta
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- Yang, Z.T., Lu, Y.F. & Cheng, Q.J. Acta. Math. Sin.-English Ser. (2017) 33: 545. doi:10.1007/s10114-017-6354-5
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We prove that a topological space is uniform Eberlein compact iff it is homeomorphic to a super weakly compact subset C of a Banach space such that the closed convex hull co̅C of C is super weakly compact. We also show that a Banach space X is super weakly compactly generated iff the dual unit ball BX* of X* in its weak star topology is affinely homeomorphic to a super weakly compactly convex subset of a Banach space.