Topological Analysis : : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / / Martin Väth.
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 mul...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2012] ©2012 |
Year of Publication: | 2012 |
Language: | English |
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Physical Description: | 1 online resource (490 p.) |
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Väth, Martin, author. aut http://id.loc.gov/vocabulary/relators/aut Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / Martin Väth. Berlin ; Boston : De Gruyter, [2012] ©2012 1 online resource (490 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Series in Nonlinear Analysis and Applications , 0941-813X ; 16 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Algebraic topology. Fredholm operators. Topological degree. Topological spaces. Degree Theory. Fredholm Maps. Function Triples. Multivalued Maps. Nonlinear Analysis. Topology. MATHEMATICS / Functional Analysis. bisacsh Analysis. Banach Manifold. Fredholm. Hahn-Banach Theorem. Implicit Function Theorem. Inverse Function Theorem. Linear Functional Analysis. Multivalued Map. Nonlinear Functional Analysis. Nonlinear Inclusion. Separation Axiom. Triple Degree. Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications 9783110647099 Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 9783110238570 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) 9783110238471 Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 9783110637205 ZDB-23-GMA Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012 9783110288995 ZDB-23-DGG Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012 9783110293722 ZDB-23-DMI Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012 9783110288926 ZDB-23-DMP print 9783110277227 https://doi.org/10.1515/9783110277333 https://www.degruyter.com/isbn/9783110277333 Cover https://www.degruyter.com/document/cover/isbn/9783110277333/original |
language |
English |
format |
eBook |
author |
Väth, Martin, Väth, Martin, |
spellingShingle |
Väth, Martin, Väth, Martin, Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / De Gruyter Series in Nonlinear Analysis and Applications , 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 |
author_facet |
Väth, Martin, Väth, Martin, |
author_variant |
m v mv m v mv |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Väth, Martin, |
title |
Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / |
title_sub |
From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / |
title_full |
Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / Martin Väth. |
title_fullStr |
Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / Martin Väth. |
title_full_unstemmed |
Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / Martin Väth. |
title_auth |
Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / |
title_alt |
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 |
title_new |
Topological Analysis : |
title_sort |
topological analysis : from the basics to the triple degree for nonlinear fredholm inclusions / |
series |
De Gruyter Series in Nonlinear Analysis and Applications , |
series2 |
De Gruyter Series in Nonlinear Analysis and Applications , |
publisher |
De Gruyter, |
publishDate |
2012 |
physical |
1 online resource (490 p.) Issued also in print. |
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 |
isbn |
9783110277333 9783110647099 9783110238570 9783110238471 9783110637205 9783110288995 9783110293722 9783110288926 9783110277227 |
issn |
0941-813X ; |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA612 |
callnumber-sort |
QA 3612 V38 42012 |
url |
https://doi.org/10.1515/9783110277333 https://www.degruyter.com/isbn/9783110277333 https://www.degruyter.com/document/cover/isbn/9783110277333/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.13 |
dewey-sort |
3515.13 |
dewey-raw |
515.13 |
dewey-search |
515.13 |
doi_str_mv |
10.1515/9783110277333 |
oclc_num |
796384299 |
work_keys_str_mv |
AT vathmartin topologicalanalysisfromthebasicstothetripledegreefornonlinearfredholminclusions |
status_str |
n |
ids_txt_mv |
(DE-B1597)175111 (OCoLC)796384299 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1 Title is part of eBook package: De Gruyter DGBA Backlist Mathematics 2000-2014 (EN) Title is part of eBook package: De Gruyter DGBA Mathematics - 2000 - 2014 Title is part of eBook package: De Gruyter E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2012 Title is part of eBook package: De Gruyter E-BOOK PACKAGE MATHEMATICS, PHYSICS, ENGINEERING 2012 Title is part of eBook package: De Gruyter E-BOOK PAKET MATHEMATIK, PHYSIK, INGENIEURWISS. 2012 |
is_hierarchy_title |
Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions / |
container_title |
Title is part of eBook package: De Gruyter DG Studies in Nonlinear Analysis and Applications |
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fullrecord |
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