| Description |
1 online resource (500 pages). |
|
text file |
| Series |
De Gruyter Series in Nonlinear Analysis and Applications ; v. 16
|
|
De Gruyter series in nonlinear analysis and applications.
|
| Contents |
Preface; 1 Introduction; I Topology and Multivalued Maps; 2 Multivalued Maps; 2.1 Notations for Multivalued Maps and Axioms; 2.1.1 Notations; 2.1.2 Axioms; 2.2 Topological Notations and Basic Results; 2.3 Separation Axioms; 2.4 Upper Semicontinuous Multivalued Maps; 2.5 Closed and Proper Maps; 2.6 Coincidence Point Sets and Closed Graphs; 3 Metric Spaces; 3.1 Notations and Basic Results for Metric Spaces; 3.2 Three Measures of Noncompactness; 3.3 Condensing Maps; 3.4 Convexity; 3.5 Two Embedding Theorems for Metric Spaces; 3.6 Some Old and New Extension Theorems for Metric Spaces. |
|
4 Spaces Defined by Extensions, Retractions, or Homotopies4.1 AE and ANE Spaces; 4.2 ANR and AR Spaces; 4.3 Extension of Compact Maps and of Homotopies; 4.4 UV8 and Rd Spaces and Homotopic Characterizations; 5 Advanced Topological Tools; 5.1 Some Covering Space Theory; 5.2 A Glimpse on Dimension Theory; 5.3 Vietoris Maps; II Coincidence Degree for Fredholm Maps; 6 Some Functional Analysis; 6.1 Bounded Linear Operators and Projections; 6.2 Linear Fredholm Operators; 7 Orientation of Families of Linear Fredholm Operators; 7.1 Orientation of a Linear Fredholm Operator. |
|
7.2 Orientation of a Continuous Family7.3 Orientation of a Family in Banach Bundles; 8 Some Nonlinear Analysis; 8.1 The Pointwise Inverse and Implicit Function Theorems; 8.2 Oriented Nonlinear Fredholm Maps; 8.3 Oriented Fredholm Maps in Banach Manifolds; 8.4 A Partial Implicit Function Theorem in Banach Manifolds; 8.5 Transversal Submanifolds; 8.6 Parameter-Dependent Transversality and Partial Submanifolds; 8.7 Orientation on Submanifolds and on Partial Submanifolds; 8.8 Existence of Transversal Submanifolds; 8.9 Properness of Fredholm Maps; 9 The Brouwer Degree. |
|
9.1 Finite-Dimensional Manifolds9.2 Orientation of Continuous Maps and of Manifolds; 9.3 The Cr Brouwer Degree; 9.4 Uniqueness of the Brouwer Degree; 9.5 Existence of the Brouwer Degree; 9.6 Some Classical Applications of the Brouwer Degree; 10 The Benevieri-Furi Degrees; 10.1 Further Properties of the Brouwer Degree; 10.2 The Benevieri-Furi C1 Degree; 10.3 The Benevieri-Furi Coincidence Degree; III Degree Theory for Function Triples; 11 Function Triples; 11.1 Function Triples and Their Equivalences; 11.2 The Simplifier Property; 11.3 Homotopies of Triples; 11.4 Locally Normal Triples. |
|
12 The Degree for Finite-Dimensional Fredholm Triples12.1 The Triple Variant of the Brouwer Degree; 12.2 The Triple Variant of the Benevieri-Furi Degree; 13 The Degree for Compact Fredholm Triples; 13.1 The Leray-Schauder Triple Degree; 13.2 The Leray-Schauder Coincidence Degree; 13.3 Classical Applications of the Leray-Schauder Degree; 14 The Degree for Noncompact Fredholm Triples; 14.1 The Degree for Fredholm Triples with Fundamental Sets; 14.2 Homotopic Tests for Fundamental Sets; 14.3 The Degree for Fredholm Triples with Convex-fundamental Sets; 14.4 Countably Condensing Triples. |
| Note |
14.5 Classical Applications in the General Framework. |
| Summary |
This monograph is an introduction to some special aspects of topology, functional analysis, and analysis for the advanced reader. It also wants to develop a degree theory for function triples which unifies and extends most known degree theories. The book aims to be self-contained and many chapters could even serve as a basis of a course on the covered topics. Only knowledge in basic calculus and of linear algebra is assumed. |
| Bibliography |
Includes bibliographical references and indexes. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Topological degree.
|
|
Topological degree. |
|
Topological spaces.
|
|
Topological spaces. |
|
Fredholm operators.
|
|
Fredholm operators. |
|
Algebraic topology.
|
|
Algebraic topology. |
| Genre/Form |
Electronic books.
|
| Other Form: |
Print version: Väth, Martin. Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions. Berlin : De Gruyter, ©2012 9783110277227 |
| ISBN |
9783110277340 |
|
3110277344 |
|
9783110277333 |
|
3110277336 |
|
9783110277227 (hardcover ; alkaline paper) |
|
3110277220 (hardcover ; alkaline paper) |
|
