Topological Analysis

1 - Preface [Seite 5]
2 - 1 Introduction [Seite 11]
3 - I Topology and Multivalued Maps [Seite 17]
3.1 - 2 Multivalued Maps [Seite 19]
3.1.1 - 2.1 Notations for Multivalued Maps and Axioms [Seite 19]
3.1.1.1 - 2.1.1 Notations [Seite 19]
3.1.1.2 - 2.1.2 Axioms [Seite 21]
3.1.2 - 2.2 Topological Notations and Basic Results [Seite 27]
3.1.3 - 2.3 Separation Axioms [Seite 34]
3.1.4 - 2.4 Upper Semicontinuous Multivalued Maps [Seite 53]
3.1.5 - 2.5 Closed and Proper Maps [Seite 62]
3.1.6 - 2.6 Coincidence Point Sets and Closed Graphs [Seite 65]
3.2 - 3 Metric Spaces [Seite 69]
3.2.1 - 3.1 Notations and Basic Results for Metric Spaces [Seite 69]
3.2.2 - 3.2 Three Measures of Noncompactness [Seite 77]
3.2.3 - 3.3 Condensing Maps [Seite 85]
3.2.4 - 3.4 Convexity [Seite 94]
3.2.5 - 3.5 Two Embedding Theorems for Metric Spaces [Seite 99]
3.2.6 - 3.6 Some Old and New Extension Theorems for Metric Spaces [Seite 106]
3.3 - 4 Spaces Defined by Extensions, Retractions, or Homotopies [Seite 115]
3.3.1 - 4.1 AE and ANE Spaces [Seite 115]
3.3.2 - 4.2 ANR and AR Spaces [Seite 117]
3.3.3 - 4.3 Extension of Compact Maps and of Homotopies [Seite 124]
3.3.4 - 4.4 UV8 and Rd Spaces and Homotopic Characterizations [Seite 132]
3.4 - 5 Advanced Topological Tools [Seite 139]
3.4.1 - 5.1 Some Covering Space Theory [Seite 139]
3.4.2 - 5.2 A Glimpse on Dimension Theory [Seite 143]
3.4.3 - 5.3 Vietoris Maps [Seite 150]
4 - II Coincidence Degree for Fredholm Maps [Seite 155]
4.1 - 6 Some Functional Analysis [Seite 157]
4.1.1 - 6.1 Bounded Linear Operators and Projections [Seite 157]
4.1.2 - 6.2 Linear Fredholm Operators [Seite 170]
4.2 - 7 Orientation of Families of Linear Fredholm Operators [Seite 179]
4.2.1 - 7.1 Orientation of a Linear Fredholm Operator [Seite 179]
4.2.2 - 7.2 Orientation of a Continuous Family [Seite 188]
4.2.3 - 7.3 Orientation of a Family in Banach Bundles [Seite 192]
4.3 - 8 Some Nonlinear Analysis [Seite 207]
4.3.1 - 8.1 The Pointwise Inverse and Implicit Function Theorems [Seite 207]
4.3.2 - 8.2 Oriented Nonlinear Fredholm Maps [Seite 213]
4.3.3 - 8.3 Oriented Fredholm Maps in Banach Manifolds [Seite 214]
4.3.4 - 8.4 A Partial Implicit Function Theorem in Banach Manifolds [Seite 224]
4.3.5 - 8.5 Transversal Submanifolds [Seite 230]
4.3.6 - 8.6 Parameter-Dependent Transversality and Partial Submanifolds [Seite 236]
4.3.7 - 8.7 Orientation on Submanifolds and on Partial Submanifolds [Seite 239]
4.3.8 - 8.8 Existence of Transversal Submanifolds [Seite 241]
4.3.9 - 8.9 Properness of Fredholm Maps [Seite 244]
4.4 - 9 The Brouwer Degree [Seite 247]
4.4.1 - 9.1 Finite-Dimensional Manifolds [Seite 247]
4.4.2 - 9.2 Orientation of Continuous Maps and of Manifolds [Seite 258]
4.4.3 - 9.3 The Cr Brouwer Degree [Seite 265]
4.4.4 - 9.4 Uniqueness of the Brouwer Degree [Seite 271]
4.4.5 - 9.5 Existence of the Brouwer Degree [Seite 289]
4.4.6 - 9.6 Some Classical Applications of the Brouwer Degree [Seite 303]
4.5 - 10 The Benevieri-Furi Degrees [Seite 319]
4.5.1 - 10.1 Further Properties of the Brouwer Degree [Seite 320]
4.5.2 - 10.2 The Benevieri-Furi C1 Degree [Seite 328]
4.5.3 - 10.3 The Benevieri-Furi Coincidence Degree [Seite 334]
5 - III Degree Theory for Function Triples [Seite 347]
5.1 - 11 Function Triples [Seite 349]
5.1.1 - 11.1 Function Triples and Their Equivalences [Seite 351]
5.1.2 - 11.2 The Simplifier Property [Seite 365]
5.1.3 - 11.3 Homotopies of Triples [Seite 371]
5.1.4 - 11.4 Locally Normal Triples [Seite 375]
5.2 - 12 The Degree for Finite-Dimensional Fredholm Triples [Seite 377]
5.2.1 - 12.1 The Triple Variant of the Brouwer Degree [Seite 377]
5.2.2 - 12.2 The Triple Variant of the Benevieri-Furi Degree [Seite 390]
5.3 - 13 The Degree for Compact Fredholm Triples [Seite 401]
5.3.1 - 13.1 The Leray-Schauder Triple Degree [Seite 401]
5.3.2 - 13.2 The Leray-Schauder Coincidence Degree [Seite 414]
5.3.3 - 13.3 Classical Applications of the Leray-Schauder Degree [Seite 417]
5.4 - 14 The Degree for Noncompact Fredholm Triples [Seite 423]
5.4.1 - 14.1 The Degree for Fredholm Triples with Fundamental Sets [Seite 424]
5.4.2 - 14.2 Homotopic Tests for Fundamental Sets [Seite 439]
5.4.3 - 14.3 The Degree for Fredholm Triples with Convex-fundamental Sets [Seite 447]
5.4.4 - 14.4 Countably Condensing Triples [Seite 458]
5.4.5 - 14.5 Classical Applications in the General Framework [Seite 466]
5.4.6 - 14.6 A Sample Application for Boundary Value Problems [Seite 472]
6 - Bibliography [Seite 475]
7 - Index of Symbols [Seite 485]
8 - Index [Seite 487]