### Chebyshev centers, E-Chebyshev centers and the Hausdorff metric.

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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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