Skip to main content

Topologies on Closed and Closed Convex Sets

  • Book
  • © 1993


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

This is a preview of subscription content, log in via an institution to check access.

Access this book

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

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.

Similar content being viewed by others


Table of contents (8 chapters)

Authors and Affiliations

  • Department of Mathematics and Computer Science, California State University, Los Angeles, USA

    Gerald Beer

Bibliographic Information

  • Book Title: Topologies on Closed and Closed Convex Sets

  • Authors: Gerald Beer

  • Series Title: Mathematics and Its Applications

  • DOI:

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1993

  • Hardcover ISBN: 978-0-7923-2531-4Published: 31 October 1993

  • Softcover ISBN: 978-90-481-4333-7Published: 15 December 2010

  • eBook ISBN: 978-94-015-8149-3Published: 12 June 2019

  • Edition Number: 1

  • Number of Pages: XII, 340

  • Topics: Topology, Functional Analysis, Optimization

Publish with us