Topological Analysis : : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / / Martin Väth.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications
• VerfasserIn: Väth, Martin,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2012]; ©2012
• Year of Publication: 2012
• Language: English
• Series: De Gruyter Series in Nonlinear Analysis and Applications , 16
• Physical Description: 1 online resource (490 p.)

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.

Table of Contents

Frontmatter -- 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