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Sinopsis
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.
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Reseña del editor
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.
"Sobre este título" puede pertenecer a otra edición de este libro.
- EditorialSpringer
- Año de publicación2010
- ISBN 10 9048143330
- ISBN 13 9789048143337
- EncuadernaciónTapa blanda
- IdiomaInglés
- Número de páginas356
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Topologies on Closed and Closed Convex Sets
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Springer Netherlands, 2010
ISBN 10: 9048143330
ISBN 13: 9789048143337
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Topologies on Closed and Closed Convex Sets (Mathematics and Its Applications)
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Topologies on Closed and Closed Convex Sets
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Springer Netherlands, 2010
ISBN 10: 9048143330
ISBN 13: 9789048143337
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 converge. Nº de ref. del artículo: 5818197
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Topologies on Closed and Closed Convex Sets (Paperback or Softback)
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Springer 12/15/2010, 2010
ISBN 10: 9048143330
ISBN 13: 9789048143337
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Topologies on Closed and Closed Convex Sets
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Springer Netherlands, 2010
ISBN 10: 9048143330
ISBN 13: 9789048143337
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Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Nº de ref. del artículo: 9789048143337
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Topologies on Closed and Closed Convex Sets (Mathematics and Its Applications)
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Topologies on Closed and Closed Convex Sets
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Topologies on Closed and Closed Convex Sets
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Topologies on Closed and Closed Convex Sets
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Topologies on Closed and Closed Convex Sets (Mathematics and Its Applications)
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