Topological Analysis
From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions
Seiten
| Ausstattung: Hardcover & eBook
2012
De Gruyter
9783110277340 (ISBN)
De Gruyter
9783110277340 (ISBN)
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The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jürgen Appell.
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.
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.
Martin Väth, Freie Universität Berlin, Germany.
| Reihe/Serie | De Gruyter Series in Nonlinear Analysis and Applications ; 16 |
|---|---|
| Zusatzinfo | Includes a print version and an ebook |
| Verlagsort | Berlin/Boston |
| Sprache | englisch |
| Maße | 170 x 240 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Schlagworte | Analysis • Banach Manifold • Degree Theory • Fredholm • Fredholm Maps • Function Triples • Hahn-Banach theorem • implicit function theorem • inverse function theorem • Linear Functional Analysis • Multivalued Map • multivalued maps • Nonlinear analysis • nonlinear functional analysis • Nonlinear Inclusion • Separation axiom • Topology • Topology; Analysis; Triple Degree; Nonlinear Inclusion; Fredholm; Linear Functional Analysis; Nonlinear Functional Analysis; Multivalued Map; Separation Axiom; Inverse Function Theorem; Implicit Function Theorem; Hahn-Banach Theorem; Banach Manifold • Triple Degree |
| ISBN-13 | 9783110277340 / 9783110277340 |
| Zustand | Neuware |
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