1# Library to Find Best eBook for Read
Author : Walter Roelcke
Release : 1981
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Uniform Structures on Topological Groups and Their Quotients by : Walter Roelcke
Download or read book Uniform Structures on Topological Groups and Their Quotients written by Walter Roelcke. This book was released on 1981. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. V. Arkhangelʹskiĭ
Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 066/5 ( reviews)
Book Synopsis Topological Groups and Related Structures by : A. V. Arkhangelʹskiĭ
Download or read book Topological Groups and Related Structures written by A. V. Arkhangelʹskiĭ. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, the objects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groups and semigroups, paratopological groups, etc. Special emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of the operation. The main scope of the book, however, is outside of the locally compact structures, thus distinguishing the monograph from a series of more traditional textbooks.The book is unique in that it presents very important material, dispersed in hundreds of research articles, not covered by any monograph in existence. The reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the way to the frontier of the knowledge is quite short -- almost every section of the book contains several intriguing open problems whose solutions can contribute significantly to the area.
Author : I. M. James
Release : 1990-05-03
Genre : Mathematics
Kind : eBook
Book Rating : 203/5 ( reviews)
Book Synopsis Introduction to Uniform Spaces by : I. M. James
Download or read book Introduction to Uniform Spaces written by I. M. James. This book was released on 1990-05-03. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course taught to an audience of undergraduate and graduate students at Oxford, and can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, much of which is published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces. Readers interested in general topology will find much to interest them here.
Author : Alexander Arhangel’skii
Release : 2008-05-01
Genre : Mathematics
Kind : eBook
Book Rating : 35X/5 ( reviews)
Book Synopsis Topological Groups and Related Structures, An Introduction to Topological Algebra. by : Alexander Arhangel’skii
Download or read book Topological Groups and Related Structures, An Introduction to Topological Algebra. written by Alexander Arhangel’skii. This book was released on 2008-05-01. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Christian Rosendal
Release : 2021-12-16
Genre : Mathematics
Kind : eBook
Book Rating : 196/5 ( reviews)
Book Synopsis Coarse Geometry of Topological Groups by : Christian Rosendal
Download or read book Coarse Geometry of Topological Groups written by Christian Rosendal. This book was released on 2021-12-16. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general framework for doing geometric group theory for many non-locally-compact topological transformation groups that arise in mathematical practice, including homeomorphism and diffeomorphism groups of manifolds, isometry groups of separable metric spaces and automorphism groups of countable structures. Using Roe's framework of coarse structures and spaces, the author defines a natural coarse geometric structure on all topological groups. This structure is accessible to investigation, especially in the case of Polish groups, and often has an explicit description, generalising well-known structures in familiar cases including finitely generated discrete groups, compactly generated locally compact groups and Banach spaces. In most cases, the coarse geometric structure is metrisable and may even be refined to a canonical quasimetric structure on the group. The book contains many worked examples and sufficient introductory material to be accessible to beginning graduate students. An appendix outlines several open problems in this young and rich theory.
