This monograph provides an 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 as well. A unifying theme is the
relationship between topology and set convergence on the one hand, and
set functionals on the other. The text includes for the first time
anywhere an exposition of three topologies that over the past ten years
have become fundamental tools in optimization, one-sided analysis,
convex analysis, and the theory of multifunctions: the Wijsman topology,
the Attouch--Wets topology, and the slice topology. Particular attention
is given to topologies on lower semicontinuous functions, especially
lower semicontinuous convex functions, as associated with their
epigraphs. The interplay between convex duality and topology is
carefully considered and a chapter on set-valued functions is included.
The book contains over 350 exercises and is suitable as a graduate
text.
This book is of interest to those working in general topology,
set-valued analysis, geometric functional analysis, optimization, convex
analysis and mathematical economics.