© 1993

Topologies on Closed and Closed Convex Sets


Part of the Mathematics and Its Applications book series (MAIA, volume 268)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Gerald Beer
    Pages 1-33
  3. Gerald Beer
    Pages 183-234
  4. Gerald Beer
    Pages 270-305
  5. Back Matter
    Pages 306-340

About this book


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.


Mathematica functional analysis optimization set topology

Authors and affiliations

  1. 1.Department of Mathematics and Computer ScienceCalifornia State UniversityLos AngelesUSA

Bibliographic information

  • Book Title Topologies on Closed and Closed Convex Sets
  • Authors Gerald Beer
  • Series Title Mathematics and Its Applications
  • DOI
  • Copyright Information Springer Science+Business Media Dordrecht 1993
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-7923-2531-4
  • Softcover ISBN 978-90-481-4333-7
  • eBook ISBN 978-94-015-8149-3
  • Edition Number 1
  • Number of Pages XII, 340
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Topology
    Functional Analysis
  • Buy this book on publisher's site