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Book review

Author(s) Beer, G.
Title Topologies on closed and closed convex sets
Publisher Kluwer Academic Publishers
Year of publication 1993
Reviewed by Gh. Toader

This monograph is an advanced introduction to the theory of topologies defined on the closed subsets of a metric space and on the closed convex subsets of a normed linear space. It includes for the first time an exposition of the Wijsman topology , the Attouch-Wets topology and the slice topology beside other topologies like the Hausdorff metric topology, the Fell topology or the Mosco topology. The last three chapters are devoted to multifunctions, especially to topologies on lower semicontinuous convex functions.

The author is well known as an expert in the field. The book is very well written, almost exhaustive, and has many historical commentaries and exercises (over 350). The list of references contains more than 430 titles.

Obviously this book will be useful to specialists in set-valued analysis, convex analysis or optimization and cannot miss from any library.