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Dentability and extreme points. (English) Zbl 0819.46012

Summary: We prove that in a separable Banach space \(X\), if every bounded closed subset \(K\) of \(X\) with \(K\subset U(X)\) and \(\overline{\text{co}}(K)= U(X)\) contains an extreme point of \(\text{co}(K)\), then \(U(X)\) must be dentable, and that if \(U(X)\) has denting points, then every weak closed bounded subset \(K\) of \(X\) with \(K\subset U(X)\) and \(\overline{\text{co}}(K)= U(X)\) contains an extreme point of \(\text{co}(K)\).

MSC:

46B22 Radon-Nikodým, Kreĭn-Milman and related properties
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