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Topologies And Uniformities
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Book Synopsis Topologies and Uniformities by : Ioan M. James
Download or read book Topologies and Uniformities written by Ioan M. James and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A substantially revised edition of the UTM volume, with a view to making the book far more accessible to undergraduates. It contains a larger number of detailed explanations and exercises, together with fully worked solutions to the essential problems and a new chapter on the historical aspects.
Book Synopsis General Topology by : Stephen Willard
Download or read book General Topology written by Stephen Willard and published by Courier Corporation. This book was released on 2012-07-12 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.
Book Synopsis Introduction to Uniform Spaces by : I. M. James
Download or read book Introduction to Uniform Spaces written by I. M. James and published by Cambridge University Press. This book was released on 1990-05-03 with total page 160 pages. 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.
Book Synopsis Lectures on Coarse Geometry by : John Roe
Download or read book Lectures on Coarse Geometry written by John Roe and published by American Mathematical Soc.. This book was released on 2003 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coarse geometry is the study of spaces (particularly metric spaces) from a 'large scale' point of view, so that two spaces that look the same from a great distance are actually equivalent. This book provides a general perspective on coarse structures. It discusses results on asymptotic dimension and uniform embeddings into Hilbert space.
Book Synopsis Handbook of the History of General Topology by : C.E. Aull
Download or read book Handbook of the History of General Topology written by C.E. Aull and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.
Book Synopsis Modern Analysis and Topology by : Norman R. Howes
Download or read book Modern Analysis and Topology written by Norman R. Howes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. It is intended that the material be accessible to a reader of modest background. An advanced calculus course and an introductory topology course should be adequate. But it is also intended that this book be able to take the reader from that state to the frontiers of modern analysis and topology in-so-far as they can be done within the framework of uniform spaces. Modern analysis is usually developed in the setting of metric spaces although a great deal of harmonic analysis is done on topological groups and much offimctional analysis is done on various topological algebraic structures. All of these spaces are special cases of uniform spaces. Modern topology often involves spaces that are more general than uniform spaces, but the uniform spaces provide a setting general enough to investigate many of the most important ideas in modern topology, including the theories of Stone-Cech compactification, Hewitt Real-compactification and Tamano-Morita Para compactification, together with the theory of rings of continuous functions, while at the same time retaining a structure rich enough to support modern analysis.
Book Synopsis Encyclopedia of General Topology by : K.P. Hart
Download or read book Encyclopedia of General Topology written by K.P. Hart and published by Elsevier. This book was released on 2003-11-18 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book.Key features:• More terms from General Topology than any other book ever published• Short and informative articles• Authors include the majority of top researchers in the field• Extensive indexing of terms
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1993-01-31 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis General Topology by : John L. Kelley
Download or read book General Topology written by John L. Kelley and published by Courier Dover Publications. This book was released on 2017-03-17 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure," noted the Bulletin of the American Mathematical Society upon the 1955 publication of John L. Kelley's General Topology. This comprehensive treatment for beginning graduate-level students immediately found a significant audience, and it remains a highly worthwhile and relevant book for students of topology and for professionals in many areas. A systematic exposition of the part of general topology that has proven useful in several branches of mathematics, this volume is especially intended as background for modern analysis. An extensive preliminary chapter presents mathematical foundations for the main text. Subsequent chapters explore topological spaces, the Moore-Smith convergence, product and quotient spaces, embedding and metrization, and compact, uniform, and function spaces. Each chapter concludes with an abundance of problems, which form integral parts of the discussion as well as reinforcements and counter examples that mark the boundaries of possible theorems. The book concludes with an extensive index that provides supplementary material on elementary set theory.
Download or read book General Topology written by N. Bourbaki and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the softcover reprint of the 1971 English translation of the first four chapters of Bourbaki’s Topologie Generale. It gives all basics of the subject, starting from definitions. Important classes of topological spaces are studied, and uniform structures are introduced and applied to topological groups. In addition, real numbers are constructed and their properties established.
Book Synopsis General Topology III by : A. V. Arhangel' skii
Download or read book General Topology III written by A. V. Arhangel' skii and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference work deals with important topics in general topology and their role in functional analysis and axiomatic set theory, for graduate students and researchers working in topology, functional analysis, set theory and probability theory. It provides a guide to recent research findings, with three contributions by Arhangel'skii and Choban.
Download or read book Topological Algebras written by and published by Elsevier. This book was released on 2011-10-10 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c). It characterizes the maximal ideals and homomorphisms closed maximal ideals and continuous homomorphisms of topological algebras in general and C(T,F,c) in particular. A considerable inroad is made into the properties of C(T,F,c) as a topological vector space. Many of the results about C(T,F,c) serve to illustrate and motivate results about general topological algebras. Attention is restricted to the algebra C(T,R) of real-valued continuous functions and to the pursuit of the maximal ideals and real-valued homomorphisms of such algebras. The chapter presents the correlation of algebraic properties of C(T,F) with purely topological properties of T. The Stone–Cech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.
Book Synopsis Topological and Uniform Spaces by : I.M. James
Download or read book Topological and Uniform Spaces written by I.M. James and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures I have given to undergraduate and graduate audiences at Oxford and elsewhere over the years. My aim has been to provide an outline of both the topological theory and the uniform theory, with an emphasis on the relation between the two. Although I hope that the prospec tive specialist may find it useful as an introduction it is the non-specialist I have had more in mind in selecting the contents. Thus I have tended to avoid the ingenious examples and counterexamples which often occupy much ofthe space in books on general topology, and I have tried to keep the number of definitions down to the essential minimum. There are no particular pre requisites but I have worked on the assumption that a potential reader will already have had some experience of working with sets and functions and will also be familiar with the basic concepts of algebra and analysis. There are a number of fine books on general topology, some of which I have listed in the Select Bibliography at the end of this volume. Of course I have benefited greatly from this previous work in writing my own account. Undoubtedly the strongest influence is that of Bourbaki's Topologie Generale [2], the definitive treatment of the subject which first appeared over a genera tion ago.
Book Synopsis Function Spaces with Uniform, Fine and Graph Topologies by : Robert A. McCoy
Download or read book Function Spaces with Uniform, Fine and Graph Topologies written by Robert A. McCoy and published by Springer. This book was released on 2018-04-21 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing literature. The goal of this monograph is to provide an extensive study of the uniform, fine and graph topologies on the space C(X,Y) of all continuous functions from a Tychonoff space X to a metric space (Y,d); and the uniform and fine topologies on the space H(X) of all self-homeomorphisms on a metric space (X,d). The subject matter of this monograph is significant from the theoretical viewpoint, but also has applications in areas such as analysis, approximation theory and differential topology. Written in an accessible style, this book will be of interest to researchers as well as graduate students in this vibrant research area.
Book Synopsis Advances in Topology and Their Interdisciplinary Applications by : Santanu Acharjee
Download or read book Advances in Topology and Their Interdisciplinary Applications written by Santanu Acharjee and published by Springer Nature. This book was released on 2023-05-09 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains selected chapters on recent research in topology. It bridges the gap between recent trends of topological theories and their applications in areas like social sciences, natural sciences, soft computing, economics, theoretical chemistry, cryptography, pattern recognitions and granular computing. There are 14 chapters, including two chapters on mathematical economics from the perspective of topology. The book discusses topics on function spaces, relator space, preorder, quasi-uniformities, bitopological dynamical systems, b-metric spaces and related fixed point theory. This book is useful to researchers, experts and scientists in studying the cutting-edge research in topology and related areas and helps them applying topology in solving real-life problems the society and science are facing these days.
Download or read book General Topology written by Tom Richmond and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-07-06 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first half of the book provides an introduction to general topology, with ample space given to exercises and carefully selected applications. The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science. Recurring themes include the interactions of topology with order theory and mathematics designed to model loss-of-resolution situations.
Book Synopsis Real Analysis and Probability by : R. M. Dudley
Download or read book Real Analysis and Probability written by R. M. Dudley and published by CRC Press. This book was released on 2018-02-01 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the best-known probabilists in the world this text offers a clear and modern presentation of modern probability theory and an exposition of the interplay between the properties of metric spaces and those of probability measures. This text is the first at this level to include discussions of the subadditive ergodic theorems, metrics for convergence in laws and the Borel isomorphism theory. The proofs for the theorems are consistently brief and clear and each chapter concludes with a set of historical notes and references. This book should be of interest to students taking degree courses in real analysis and/or probability theory.
