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On Mosco convergence of convex sets

Published online by Cambridge University Press:  17 April 2009

Gerald Beer
Gerald Beer
Affiliation:
Department of Mathematics, California State University, Los Angeles, Los Angeles, CA 90032, United States of America
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 2 , October 1988 , pp. 239 - 253
Copyright
Copyright © Australian Mathematical Society 1988

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