Topological analysis : from the basics to the triple degree for nonlinear Fredholm inclusions / Martin Väth.

Format:

Book

Author/Creator:

Väth, Martin, 1967-

Series:

De Gruyter series in nonlinear analysis and applications ; 16.

De Gruyter series in nonlinear analysis and applications, 0941-813X ; 16

Language:

English

Subjects (All):

Topological degree.

Topological spaces.

Fredholm operators.

Algebraic topology.

Physical Description:

1 online resource (500 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, c2012.

Language Note:

English

Summary:

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.

Contents:

Front matter

Preface

Contents

Chapter 1. Introduction

Part I. Topology and Multivalued Maps

Chapter 2. Multivalued Maps

Chapter 3. Metric Spaces

Chapter 4. Spaces Defined by Extensions, Retractions, or Homotopies

Chapter 5. Advanced Topological Tools

Part II. Coincidence Degree for Fredholm Maps

Chapter 6. Some Functional Analysis

Chapter 7. Orientation of Families of Linear Fredholm Operators

Chapter 8. Some Nonlinear Analysis

Chapter 9. The Brouwer Degree

Chapter 10. The Benevieri-Furi Degrees

Part III. Degree Theory for Function Triples

Chapter 11. Function Triples

Chapter 12. The Degree for Finite-Dimensional Fredholm Triples

Chapter 13. The Degree for Compact Fredholm Triples

Chapter 14. The Degree for Noncompact Fredholm Triples

Bibliography

Index of Symbols

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and indexes.

ISBN:

1-283-85794-4

3-11-027734-4

OCLC:

796384299