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

Martin Väth

ISBN 10: 3110277220 / ISBN 13: 9783110277227

Editore: De Gruyter, 2012

Riguardo questo articolo

Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783110277227

Dati bibliografici

• Titolo: Topological Analysis : From the Basics to the Triple Degree for Nonlinear Fredholm Inclusions
• Editore: De Gruyter
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3110277220
• ISBN 13: 9783110277227
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 246 L x 175 A x 40 P (millimetri) 246 millimetri di larghezza per 175 millimetri di altezza per 40 millimetri di profondità
• Peso: 1122 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

Martin Väth, Freie Universität Berlin, Germany.