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Topologie Générale : Chapitres 5 à 10 = General Topology : Chapters 5 to 10
Nicolas BOURBAKI's Elements of Mathematics aim at a rigorous, systematic presentation without prerequisites of mathematics from their foundations.This second volume of the Book of General Topology, third Book of the treaty, describes many fundamental tools in topology and analysis, such as than Urysohn's theorem, Baire's theorem or Polish spaces.
Topologie générale : Chapitres 1 à 4 = General topology : Chapters 1 to 4
Nicolas BOURBAKI's Elements of Mathematics aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. of Analysis and Geometry. It also contains historical notes. This volume is a reprint of the 1971 edition.
Topological Quantum Field Theory and Four Manifolds
Deals with topological quantum field theories and their applications to topological aspects of four manifolds. This book contains a chapter dealing with topological aspects of four manifolds. It also provides an introduction to supersymmetry. It constitutes a useful tool for researchers interested in the basics of topological quantum field theory.
Topological Methods in Group Theory
Topological Methods in Group Theory is about the interplay between algebraic topology and the theory of infinite discrete groups. The author has kept three kinds of readers in mind: graduate students who have had an introductory course in algebraic topology and who need a bridge from common knowledge to the current research literature in geometric, combinatorial and homological group theory; group theorists who would like to know more about the topological side of their subject but who have been too long away from topology; and manifold topologists, both high- and low-dimensional, since the book contains much basic material on proper homotopy and locally finite homology not easily found elsewhere.
Topological Invariants of Stratified Spaces
The central theme of this book is the restoration of Poincaré duality, on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety.After carefully introducing sheaf theory, derived categories, Verdier duality, stratification theories, intersection homology, t-structures and perverse sheaves, the ultimate objective is to explain the construction as well as algebraic and geometric properties of invariants such as the signature and characteristic classes effectuated by self-dual sheaves.
Topological Fixed Point Theory of Multivalued Mappings
This book is devoted to the topological fixed point theory of multivalued mappings including applications to differential inclusions and mathematical economy. It is the first monograph dealing with the fixed point theory of multivalued mappings in metric ANR spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Current results are presented." "This book will be especially useful for post-graduate students and researchers interested in fixed point theory, and in particular, topological methods in nonlinear analysis, differential equations and dynamical systems.
Topological Degree Approach to Bifurcation Problems
Topological bifurcation theory is one of the most essential topics in mathematics. This book contains original bifurcation results for the existence of oscillations and chaotic behaviour of differential equations and discrete dynamical systems under variation of involved parameters. Using topological degree theory and a perturbation approach in dynamical systems, a broad variety of nonlinear problems are studied, including: non-smooth mechanical systems with dry frictions; weakly coupled oscillators; systems with relay hysteresis; differential equations on infinite lattices of Frenkel-Kontorova and discretized Klein-Gordon types; blue sky catastrophes for reversible dynamical systems; buckling of beams; and discontinuous wave equations.
Topological Data Analysis for Genomics and Evolution : Topology in Biology
Biology has entered the age of Big Data. A technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce comparisons of shape to a comparison of algebraic invariants, such as numbers, which are typically easier to work with. Topological data analysis is a rapidly developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer, and single cell characterization of developmental processes.
Topological and Bivariant K-theory
Topological K-theory is one of the most important invariants for noncommutative algebras equipped with a suitable topology or bornology. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory.We describe a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, we discuss other approaches to bivariant K-theories for operator algebras.
Topologia
Nato dall’esperienza dell’autore nell’insegnamento della topologia agli studenti del corso di Laurea in Matematica, questo libro contiene le nozioni fondamentali di topologia generale ed una introduzione alla topologia algebrica. La scelta degli argomenti, il loro ordine di presentazione e, soprattutto, il tipo di esposizione tiene conto delle tendenze attuali nell’insegnamento della topologia e delle novita’ nella struttura dei corsi di Laurea scientifici conseguenti all’introduzione del sistema 3+2. Il libro contiene circa 400 esercizi, in parte risolti.
Topographical and pathotopographical medical atlas of the pelvis, spine, and limbs
This series of atlases of topographic and pathotopographic human anatomy is a fundamental and practically important book designed for doctors of all specializations and students of medical schools. Here you can find almost everything that is connected with the topographic and pathotopographic human anatomy, including original graphs of logical structures of topographic anatomy and development of congenital abnormalities, topography of different areas in layers, pathotopography, computer and magnetic resonance imaging (MRI) of topographic and pathotopographic anatomy.
Topographical and pathotopographical medical atlas of the hHuman body
This comprehensive and exhaustive medical atlas of topographic and pathotopographic human anatomy is a fundamental and practically important book designed for doctors of all specializations and students of medical schools. Here you can find almost everything that is connected with the topographic and pathotopographic human anatomy, including original graphs of logical structures of topographic anatomy and development of congenital abnormalities, topography of different areas in layers, pathotopography, computer and magnetic resonance imaging (MRI) of topographic and pathotopographic anatomy.
Topics on Concentration Phenomena and Problems with Multiple Scales
This volume includes lecture notes devoted to the asymptotic analysis of such problems when the multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes (random, in perforated domains, on fractals), and to concentration effects in Ginzburg-Landau energies and in subcritical growth problems.
Topics in Uniform Approximation of Continuous Functions
Presents the evolution of uniform approximations of continuous functions. Starting from the simple case of a real continuous function defined on a closed real interval, i.e., the Weierstrass approximation theorems, it proceeds up to the abstract case of approximation theorems in a locally convex lattice of (M) type.In turn, the book presents the approximation of continuous functions defined on a locally compact space (the functions from a weighted space) and that of continuous differentiable functions defined on ¡n. In closing, it highlights selected approximation theorems in locally convex lattices of (M) type.
Topics in the Theory of Chemical and Physical Systems ; Proceedings of the 10th European Workshop on Quantum Systems in Chemistry and Physics held at Carthage, Tunisia, in September 2005
Topics in the Theory of Chemical and Physical Systems is a collection of 14 selected papers from the scientific presentations made at the 10th European Workshop on Quantum Systems in Chemistry and Physics held at Carthage, Tunisia, in September 2005. This book encompasses a spectrum of topics in which emphasis is placed on theoretical methods in the study of chemical and physical properties of various systems: Advanced Methodologies ,Interactions and Clusters, Excited States, and Condensed Matter.
Topics in the Theory of Algebraic Function Fields
This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers, where a function field of one variable is the analogue of a finite extension of Q, the field of rational numbers.
Topics in Strangeness Nuclear Physics
This set of extensive lectures presents a balanced theoretical and experimental introduction to, and survey of, the field, addressing topics such as the production and spectroscopy of strange nuclear systems, modern approaches to the hyperon-nucleon interaction, and weak decays of hypernuclei.
Topics in Hyposonic Flow Theory
Hyposonic fluid flows, characterized by a low Mach number, are mainly linked with geophysical and environmental fluid flows. In addition they are relevant to engineers because of their connection with aerodynamics. The book brings together insights derived from mathematically rigorous results and combines them with a number of realistic fluid flow situations. Asymptotic analytic solutions for the low-Mach number cases are developed to provide both insights into the underlying physics as well as benchmarks for numerical computations.
Topics in Gravitational Dynamics : Solar, Extra-Solar and Galactic Systems
This set of lectures collects surveys of open problems in celestial dynamics and dynamical astronomy applied to solar, extra-solar and galactic systems. Emphasis is on questions of stability of planetary systems.
Topics in Geometry, Coding Theory and Cryptography
This book presents survey articles on some of these new developments. Most of the material is directly related to the interaction between function fields and their various applications; in particular the structure and the number of rational places of function fields are of great significance. The topics focus on material which has not yet been presented in other books or survey articles. Wherever applications are pointed out, a special effort has been made to present some background concerning their use.
