Overview

This book is the first systematic and comprehensive study of the theory of continuous selections of multivalued mappings. This interesting branch of modern topology was introduced by E.A. Michael in the 1950s and has since witnessed an intensive development with various applications outside topology, e.g. in geometry of Banach spaces, manifolds theory, convex sets, fixed points theory, differential inclusions, optimal control, approximation theory, and mathematical economics. The work can be used in different ways: the first part is an exposition of the basic theory, with details. The second part is a comprehensive survey of the main results. Lastly, the third part collects various kinds of applications of the theory. Audience: This volume will be of interest to graduate students and research mathematicians whose work involves general topology, convex sets and related geometric topics, functional analysis, global analysis, analysis on manifolds, manifolds and cell complexes, and mathematical economics.

Full Product Details

Author:   D. Repovs ,  P.V. Semenov
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 1998
Volume:   455
Dimensions:   Width: 15.50cm , Height: 1.90cm , Length: 23.50cm
Weight:   0.569kg
ISBN:  

9789048151110

ISBN 10:   9048151112
Pages:   359
Publication Date:   04 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

A. Theory.- §0. Preliminaries.- §1. Convex-valued selection theorem.- §2. Zero-dimensional selection theorem.- §3. Relations between Zero-dimensional and Convex-valued selection theorems.- §4. Compact-valued selection theorem.- §5. Finite-dimensional selection theorem.- §6. Examples and counterexamples.- §7. Addendum: New proof of Finite-dimensional selection theorem.- B. Results.- §1. Characterization of normality-type properties.- §2. Unified selection theorems.- §3. Selection theorems for non-lower semicontinuous mappings.- §4. Selection theorems for nonconvex-valued maps.- §5. Miscellaneous results.- §6. Measurable selections.- C. Applications.- §1. First applications.- §2. Regular mappings and locally trivial fibrations.- §3. Fixed-point theorems.- §4. Homeomorphism Group Problem.- §5. Soft mappings.- §6. Metric projections.- §7. Differential inclusions.- References.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions