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On some geometric properties concerning closed convex sets.

D. N. KutzarovaPei-Kee LinP. L. PapiniXin Tai Yu — 1991

Collectanea Mathematica

In this article, we consider the (weak) drop property, weak property (a), and property (w) for closed convex sets. Here we give some relations between those properties. Particularly, we prove that C has (weak) property (a) if and only if the subdifferential mapping of Cº is (n-n) (respectively, (n-w)) upper semicontinuous and (weak) compact valued. This gives an extension of a theorem of Giles and the first author.

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