Topological Analysis: From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions

Martin Väth

Published by De Gruyter 2012

Topological Analysis

From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions

Martin Väth

Volume 16 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110277333

Overview
Contents

About this book

This monograph aims to give a self-contained introduction into the whole field of topological analysis: Requiring essentially only basic knowledge of elementary calculus and linear algebra, it provides all required background from topology, analysis, linear and nonlinear functional analysis, and multivalued maps, containing even basic topics like separation axioms, inverse and implicit function theorems, the Hahn-Banach theorem, Banach manifolds, or the most important concepts of continuity of multivalued maps. Thus, it can be used as additional material in basic courses on such topics. The main intention, however, is to provide also additional information on some fine points which are usually not discussed in such introductory courses.

The selection of the topics is mainly motivated by the requirements for degree theory which is presented in various variants, starting from the elementary Brouwer degree (in Euclidean spaces and on manifolds) with several of its famous classical consequences, up to a general degree theory for function triples which applies for a large class of problems in a natural manner. Although it has been known to specialists that, in principle, such a general degree theory must exist, this is the first monograph in which the corresponding theory is developed in detail.

Author / Editor information

Martin Väth, Freie Universität Berlin, Germany.

Reviews

"The book invites the reader to go on a journey from the basics of topology, through the fields of multivalued maps and Fredholm operators, up to constructions of topological degrees (both those which have been known for decades as well as more recent ones) which are presented in great detail. […] The book gives a very detailed study of different topological concepts that play important roles in a modern approach to nonlinear analysis problems, with special emphasis put on the study of problems involving set-valued maps and operators. It can surely be recommended to researchers and students interested in homotopy invariants and their applications in the theory of differential equations/inclusions." Zentralblatt für Mathematik

Supplementary Materials

Contents

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Requires Authentication Unlicensed Licensed Download PDF	vii
Chapter 1. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Part I. Topology and Multivalued Maps
Chapter 2. Multivalued Maps Requires Authentication Unlicensed Licensed Download PDF	9
Chapter 3. Metric Spaces Requires Authentication Unlicensed Licensed Download PDF	59
Chapter 4. Spaces Defined by Extensions, Retractions, or Homotopies Requires Authentication Unlicensed Licensed Download PDF	105
Chapter 5. Advanced Topological Tools Requires Authentication Unlicensed Licensed Download PDF	129
Part II. Coincidence Degree for Fredholm Maps
Chapter 6. Some Functional Analysis Requires Authentication Unlicensed Licensed Download PDF	147
Chapter 7. Orientation of Families of Linear Fredholm Operators Requires Authentication Unlicensed Licensed Download PDF	169
Chapter 8. Some Nonlinear Analysis Requires Authentication Unlicensed Licensed Download PDF	197
Chapter 9. The Brouwer Degree Requires Authentication Unlicensed Licensed Download PDF	237
Chapter 10. The Benevieri–Furi Degrees Requires Authentication Unlicensed Licensed Download PDF	309
Part III. Degree Theory for Function Triples
Chapter 11. Function Triples Requires Authentication Unlicensed Licensed Download PDF	339
Chapter 12. The Degree for Finite-Dimensional Fredholm Triples Requires Authentication Unlicensed Licensed Download PDF	367
Chapter 13. The Degree for Compact Fredholm Triples Requires Authentication Unlicensed Licensed Download PDF	391
Chapter 14. The Degree for Noncompact Fredholm Triples Requires Authentication Unlicensed Licensed Download PDF	413
Bibliography Requires Authentication Unlicensed Licensed Download PDF	465
Index of Symbols Requires Authentication Unlicensed Licensed Download PDF	475
Index Requires Authentication Unlicensed Licensed Download PDF	477

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers, Lecturers, and Graduate Students in Mathematics; Academic Libraries
Pages
- Front matter: 9
- Main content: 490
Illustrations
- Illustrations: 4
Keywords: Topology; Analysis; Triple Degree; Nonlinear Inclusion; Fredholm; Linear Functional Analysis; Nonlinear Functional Analysis; Multivalued Map; Separation Axiom; Inverse Function Theorem; Implicit Function Theorem; Hahn-Banach Theorem; Banach Manifold

eBook

Published: May 29, 2012
ISBN: 9783110277333

Hardcover

Published: May 18, 2012
ISBN: 9783110277227