On Mosco convergence of convex sets
Author:
- 1 October 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 38 (2) , 239-253
Abstract
We present a natural topology compatible with the Mosco convergence of sequences of closed convex sets in a reflexive space, and characterise the topology in terms of the continuity of the distance between convex sets and fixed weakly compact ones. When the space is separable, the topology is Polish. As an application, we show that in this context, most closed convex sets are almost Chebyshev, a result that fails for the stronger Hausdorff metric topology.Keywords
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