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120625s2012 gw ob 001 0 eng d |
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|q alk. paper)
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|2 doi
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|a (OCoLC)796384299
|z (OCoLC)804049067
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|z (OCoLC)1065702693
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| 050 |
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|a QA612 .V38 2012
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| 072 |
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7 |
|a QA
|2 lcco
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| 072 |
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|a MAT
|x 037000
|2 bisacsh
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| 049 |
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|a HCDD
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| 100 |
1 |
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|a Väth, Martin.
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| 245 |
1 |
0 |
|a Topological Analysis :
|b From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions.
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| 260 |
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|a Berlin :
|b De Gruyter,
|c 2012.
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| 300 |
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|a 1 online resource (500 pages)
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| 336 |
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|a text
|b txt
|2 rdacontent
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| 337 |
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|a computer
|b c
|2 rdamedia
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| 338 |
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|a online resource
|b cr
|2 rdacarrier
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| 490 |
1 |
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|a De Gruyter Series in Nonlinear Analysis and Applications ;
|v v. 16
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| 588 |
0 |
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|a Print version record.
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| 505 |
0 |
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|a 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.
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| 505 |
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|a 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.
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| 505 |
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|a 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.
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| 505 |
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|a 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.
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| 505 |
8 |
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|a 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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| 520 |
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|a 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.
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| 504 |
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|a Includes bibliographical references and indexes.
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| 546 |
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|a English.
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| 650 |
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0 |
|a Topological degree.
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| 650 |
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0 |
|a Topological spaces.
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| 650 |
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|a Fredholm operators.
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| 650 |
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|a Algebraic topology.
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| 650 |
|
7 |
|a MATHEMATICS
|x Functional Analysis.
|2 bisacsh
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| 650 |
|
7 |
|a Algebraic topology
|2 fast
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| 650 |
|
7 |
|a Fredholm operators
|2 fast
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| 650 |
|
7 |
|a Topological degree
|2 fast
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| 650 |
|
7 |
|a Topological spaces
|2 fast
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| 650 |
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7 |
|a Analysis
|2 gnd
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| 650 |
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7 |
|a Topologische Methode
|2 gnd
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| 758 |
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|i has work:
|a Topological analysis (Text)
|1 https://id.oclc.org/worldcat/entity/E39PCFyRtqfKDqXYqXxvjyrxrC
|4 https://id.oclc.org/worldcat/ontology/hasWork
|
| 776 |
0 |
8 |
|i Print version:
|a Väth, Martin.
|t Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions.
|d Berlin : De Gruyter, ©2012
|z 9783110277227
|
| 830 |
|
0 |
|a De Gruyter series in nonlinear analysis and applications.
|
| 856 |
4 |
0 |
|u https://ebookcentral.proquest.com/lib/holycrosscollege-ebooks/detail.action?docID=893992
|y Click for online access
|
| 903 |
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|a EBC-AC
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| 994 |
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|a 92
|b HCD
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