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

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

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 c...

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Bibliographic Details
Main Author: Väth, Martin
Format: eBook
Language:English
Published: Berlin : De Gruyter, 2012.
Series:De Gruyter series in nonlinear analysis and applications.
Subjects:
Topological degree.
Topological spaces.
Fredholm operators.
Algebraic topology.
MATHEMATICS > Functional Analysis.
Algebraic topology
Fredholm operators
Topological degree
Topological spaces
Analysis
Topologische Methode
Online Access:Click for online access
Table of 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.

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