Author : Lydia Außenhofer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 392 pages
File Size : 31,26 MB
Release : 2021-11-22
Category : Mathematics
ISBN : 3110654938
This book provides an introduction to topological groups and the structure theory of locally compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality, including a completely self-contained elementary proof of the duality theorem. Further related topics and applications are treated in separate chapters and in the appendix.
Author : Dikran Dikranjan
Publisher :
Page : 412 pages
File Size : 11,85 MB
Release : 2021-11-24
Category :
ISBN : 9783110653496
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020) Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antic, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
Author : Sidney A. Morris
Publisher : Cambridge University Press
Page : 141 pages
File Size : 18,59 MB
Release : 1977-08-04
Category : Mathematics
ISBN : 0521215439
These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.
Author : Taqdir Husain
Publisher : Courier Dover Publications
Page : 241 pages
File Size : 44,81 MB
Release : 2018-02-15
Category : Mathematics
ISBN : 0486819191
Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.
Author : Alexander Arhangel’skii
Publisher : Springer Science & Business Media
Page : 794 pages
File Size : 28,10 MB
Release : 2008-05-01
Category : Mathematics
ISBN : 949121635X
Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.
Author : Sidney A. Morris
Publisher :
Page : 138 pages
File Size : 42,60 MB
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 9781107360877
These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.
Author : José M. Amigó
Publisher : Springer Nature
Page : 273 pages
File Size : 26,33 MB
Release : 2023-07-01
Category : Mathematics
ISBN : 3031300149
The book includes selected contributions presented at the "International Meeting on Functional Analysis and Continuous Optimization" held in Elche (Spain) on June 16–17, 2022. Its contents cover very recent results in functional analysis, continuous optimization and the interplay between these disciplines. Therefore, this book showcases current research on functional analysis and optimization with individual contributions, as well as new developments in both areas. As a result, the reader will find useful information and stimulating ideas.
Author : Sergei S. Akbarov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 871 pages
File Size : 31,22 MB
Release : 2022-08-22
Category : Mathematics
ISBN : 3110780968
The term “stereotype space” was introduced in 1995 and denotes a category of locally convex spaces with surprisingly elegant properties. Its study gives an unexpected point of view on functional analysis that brings this fi eld closer to other main branches of mathematics, namely, to algebra and geometry. This volume contains the foundations of the theory of stereotype spaces, with accurate definitions, formulations, proofs, and numerous examples illustrating the interaction of this discipline with the category theory, the theory of Hopf algebras, and the four big geometric disciplines: topology, differential geometry, complex geometry, and algebraic geometry.
Author : Karl H. Hofmann
Publisher : Walter de Gruyter GmbH & Co KG
Page : 1076 pages
File Size : 18,10 MB
Release : 2023-10-23
Category : Mathematics
ISBN : 3111172600
Author : J. P. May
Publisher : University of Chicago Press
Page : 262 pages
File Size : 32,5 MB
Release : 1999-09
Category : Mathematics
ISBN : 9780226511832
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
