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Mathematics and Its Applications
cover

Topologies on Closed and Closed Convex Sets

Authors: Beer, Gerald

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Hardcover $119.99
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  • ISBN 978-90-481-4333-7
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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.

Table of contents (8 chapters)

Table of contents (8 chapters)
  • Preliminaries

    Pages 1-33

    Beer, Gerald

  • Weak Topologies Determined by Distance Functionals

    Pages 34-77

    Beer, Gerald

  • The Attouch-Wets and Hausdorff Metric Topologies

    Pages 78-105

    Beer, Gerald

  • Gap and Excess Functionals and Weak Topologies

    Pages 106-137

    Beer, Gerald

  • The Fell Topology and Kuratowski-PainlevĂ© Convergence

    Pages 138-182

    Beer, Gerald

Buy this book

eBook $89.00
price for USA in USD (gross)
  • The eBook version of this title will be available soon
  • ISBN 978-94-015-8149-3
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-0-7923-2531-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.99
price for USA in USD
  • ISBN 978-90-481-4333-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topologies on Closed and Closed Convex Sets
Authors
Series Title
Mathematics and Its Applications
Series Volume
268
Copyright
1993
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-015-8149-3
DOI
10.1007/978-94-015-8149-3
Hardcover ISBN
978-0-7923-2531-4
Softcover ISBN
978-90-481-4333-7
Edition Number
1
Number of Pages
XII, 340
Topics