Kategoria BISAC: Mathematics >> Topology - General

This comprehensive book explores the intricate realm of fine potential theory. Delving into the real theory, it navigates through harmonic and subharmonic functions, addressing the famed Dirichlet problem within finely open sets of R^n. These sets are defined relative to the coarsest topology on R^n, ensuring the continuity of all subharmonic functions. This theory underwent extensive scrutiny starting from the 1970s, particularly by Fuglede, within the classical or axiomatic framework of harmonic functions. The use of methods from fine potential theory has led to solutions of important...

This book delves into the intricate world of fixed point theory, focusing on the Krasnoselskii-Mann method to tackle common fixed point problems within a finite family of quasi-nonexpansive mappings in hyperbolic metric spaces. By exploring various iterative algorithms, including the Cimmino algorithm and dynamic string-averaging methods, this volume offers a comprehensive study of convergence and approximate solutions amidst computational errors. Key concepts such as W-hyperbolic spaces, convex combinations, and set-valued inclusions are meticulously examined. The author presents a...

This book provides an introduction to the theory of connection matrices in the context of combinatorial multivector fields. The theory of connection matrices was proposed by Conley and Franzosa for classical continuous-time dynamical systems as a tool for studying connecting orbits between isolated invariant sets. It generalizes the Morse complex in Morse theory, and has found numerous applications in dynamics. Connection matrices have been and still are a challenging topic to study, as there are no complete introductory texts, and both their intricate definition and properties are scattered...

This introductory book contains a rich collection of exercises and worked examples in Metric Spaces. Other than questions in the traditional setting, plenty of True-or-False type questions and open-ended questions are included. With detailed solutions, these are highly effective in helping students gain a bird's eye view and master the subject and pitfalls better. The presentation is clear in nurturing the mathematical insights and mathematical maturity of the readers.In this book, the pictorialization or visualization of abstract situations into simple pictures is very often crucially...

'The presentation is modeled on the discursive style of the Bourbaki collective, and the coverage of topics is rich and varied. Grandis has provided a large selection of exercises and has sprinkled orienting comments throughout. For an undergraduate library where strong students seek an overview of a significant portion of mathematics, this would be an excellent acquisition. Summing up: Recommended.'Since the last century, a large part of Mathematics is concerned with the study of mathematical structures, from groups to fields and vector spaces, from...

The classical theory of Sturm sequences provides an algorithm for determining the number of roots of a polynomial with real coefficients contained in an open interval. The main purpose of this monograph is to show that a suitable generalization of the theory of Sturm sequences provides, among others: a notion of Maslov index for an algebraic loop of lagrangians defined over a commutative ring; a proof of the fundamental theorem of (algebraic) hermitian K-theory (theorem due to M. Karoubi); a proof of the theorems of (topological) Bott periodicity (in the spirit of the work of F. Latour); the...

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce premier volume du Livre de Topologie generale, troisieme Livre du traite, est consacre aux structures fondamentales en topologie, qui constituent les fondement de l analyse et de la geometrie. Il comprend les chapitres: 1. Structures topologiques; 2. Structures uniformes; 3. Groupes topologiques; 4. Nombres reels.

Il contient egalement des notes historiques.

Ce...

Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements.

Ce deuxieme volume du Livre de Topologie generale, troisieme Livre du traite, decrit de nombreux outils fondamentaux en topologie et en analyse, tels que le theoreme d'Urysohn, le theoreme de Baire ou les espaces polonais. Il comprend les chapitres: 1. Groupes a un parametre; 2. Espaces numeriques et espaces projectifs; 3. Les groupes additifs Rⁿ; 4. Nombres complexes; 5. Utilisation...

Ce livre des Elements de mathematique est consacre a la Topologie algebrique. Les quatre premiers chapitres presentent la theorie des revetements d'un espace topologique et du groupe de Poincare. On construit le revetement universel d'un espace connexe pointe delacable et on etablit l'equivalence de categories entre revetements de cet espace et actions du groupe de Poincare.

On demontre une version generale du theoreme de van Kampen exprimant le groupoide de Poincare d'un espace topologique comme un coegalisateur de diagrammes de groupoides. Dans de nombreuses situations...