Topology: An Introduction with Application to Topological Groups
Автор: Wall C. T. C. Название: A geometric introduction to topology ISBN: 0486678504 ISBN-13(EAN): 9780486678504 Издательство: Dover Рейтинг: Цена: 1144 р. Наличие на складе: Нет в наличии.
Описание: Intended to provide a first course in algebraic topology to advanced undergraduates, this book introduces homotopy theory, the duality theorem and the relation of topological ideas to other branches of pure mathematics. It is unique in not presupposing a course in general topology and in avoiding the use of simplexes. Exercises and problems at the end of each chapter. Indexes of terms and notations. 1972 edition.
Описание: This stimulating introduction employs the language of point set topology to define and discuss topological groups. It examines set-theoretic topology and its applications in function spaces as well as homotopy and the fundamental group. Well-chosen exercises and problems serve as reinforcements. 1967 edition. Includes 99 illustrations.
This advanced monograph on Galois representation theory was written by one of the world's leading algebraists. Directed at mathematics students who have completed a graduate course in introductory algebraic topology, it offers a full treatment of the subject. The first four chapters cover characteristic classes of Galois representations whose values lie in mod 2 Galois cohomology: abelian cohomology of groups, nonabelian cohomology of groups, characteristic classes of forms and algebras, and higher-dimensional characteristic classes of bilinear forms and Galois representations. Subsequent chapters explore stable homotopy and induced representations, explicit Brauer induction theory, and applications of explicit Brauer induction to Artin root numbers and local root numbers.
Описание: Designed for a one-year course in topological vector spaces, this text is geared toward advanced undergraduates and beginning graduate students of mathematics. The subjects involve properties employed by researchers in classical analysis, differential and integral equations, distributions, summability, and classical Banach and Frechet spaces. Optional problems with hints and references introduce non-locally convex spaces, Kothe-Toeplitz spaces, Banach algebra, sequentially barrelled spaces, and norming subspaces. Extensive introductory chapters cover metric ideas, Banach space, topological vector spaces, open mapping and closed graph theorems, and local convexity. Duality is the treatment's central theme, highlighted by a presentation of completeness theorems and special topics such as inductive limits, distributions, and weak compactness. More than 30 tables at the end of the book allow quick reference to theorems and counterexamples, and a rich selection of problems concludes each section.
Автор: Naber Gregory L. Название: Topological Methods in Euclidean Spaces ISBN: 0486414523 ISBN-13(EAN): 9780486414522 Издательство: Dover Рейтинг: Цена: 1144 р. Наличие на складе: Нет в наличии.
Автор: Jonathan L. Gross Название: Topological Graph Theory ISBN: 0486417417 ISBN-13(EAN): 9780486417417 Издательство: Dover Рейтинг: Цена: 1948 р. Наличие на складе: Нет в наличии.
Описание: Clear, comprehensive introduction emphasizes graph imbedding but also covers thoroughly the connections between topological graph theory and other areas of mathematics. Discussion of imbeddings into surfaces is combined with a complete proof of the classification of closed surfaces. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem -- a proof that revolutionized the field of graph theory -- and examine the genus of a group, including imbeddings of Cayley graphs. 1987 edition. Many figures.
Описание: This text covers topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, tangent spaces, vector fields and integral curves, Whitney's embedding theorem, more. Includes 88 helpful illustrations. 1982 edition.
Описание: Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text.
Автор: Mendelson, Bert Название: Introduction to topology ISBN: 0486663523 ISBN-13(EAN): 9780486663524 Издательство: Dover Рейтинг: Цена: 1718 р. Наличие на складе: Нет в наличии.
Описание: Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology. Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness. Throughout the text, Dr. Mendelson, a former Professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.