The Stone Čech Compactification

Author : R.C. Walker
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642619359

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The Stone-Čech Compactification by R.C. Walker Pdf

Recent research has produced a large number of results concerning the Stone-Cech compactification or involving it in a central manner. The goal of this volume is to make many of these results easily accessible by collecting them in a single source together with the necessary introductory material. The author's interest in this area had its origin in his fascination with the classic text Rings of Continuous Functions by Leonard Gillman and Meyer Jerison. This excellent synthesis of algebra and topology appeared in 1960 and did much to draw attention to the Stone-Cech compactification {3X as a tool to investigate the relationships between a space X and the rings C(X) and C*(X) of real-valued continuous functions. Although in the approach taken here {3X is viewed as the object of study rather than as a tool, the influence of Rings of Continuous Functions is clearly evident. Three introductory chapters make the book essentially self-contained and the exposition suitable for the student who has completed a first course in topology at the graduate level. The development of the Stone Cech compactification and the more specialized topological prerequisites are presented in the first chapter. The necessary material on Boolean algebras, including the Stone Representation Theorem, is developed in Chapter 2. A very basic introduction to category theory is presented in the beginning of Chapter 10 and the remainder of the chapter is an introduction to the methods of categorical topology as it relates to the Stone-Cech compactification.

Author : Neil Hindman,Dona Strauss
Publisher : Walter de Gruyter
Page : 610 pages
File Size : 49,5 Mb
Release : 2011-12-23
Category : Mathematics
ISBN : 9783110258356

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Algebra in the Stone-Cech Compactification by Neil Hindman,Dona Strauss Pdf

This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-Čech compactification of a discrete semigroup and its combinatorial applications, primarily in the field known as Ramsey Theory. There has been very active research in the subject dealt with by the book in the 12 years which is now included in this edition. This book is a self-contained exposition of the theory of compact right semigroups for discrete semigroups and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra, and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more.

Author : Neil Hindman,Dona Strauss
Publisher : Walter de Gruyter
Page : 508 pages
File Size : 53,7 Mb
Release : 1998
Category : Mathematics
ISBN : 311015420X

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Algebra in the Stone-Čech Compactification by Neil Hindman,Dona Strauss Pdf

In part one, assuming only a standard first year graduate school math background, Hindman (mathematics, Howard U.) and Strauss (mathematics, U. of Hull, UK) develop the basic concepts and theorems of compact right topological semigroups, the Stone-Cech compactification of a discrete space, and the extension of the semigroup operation on S to [Beta]S. Part II presents the algebra of the semigroup [Beta]S,.; Part III illustrates powerful applications to Ramsey Theory; and Part IV concludes with links to topological dynamics, ergodic theory, and the general theory of semigroup compactifications. Chapters include exercises and notes on historical development. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Russell C. Walker
Publisher : Unknown
Page : 332 pages
File Size : 48,7 Mb
Release : 195?
Category : Mathematics
ISBN : 0387066993

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Ergebnisse der Mathematik und ihrer Grenzgebiete by Russell C. Walker Pdf

Author : Neil Hindman,Dona Strauss
Publisher : Walter de Gruyter
Page : 501 pages
File Size : 44,7 Mb
Release : 2011-04-20
Category : Mathematics
ISBN : 9783110809220

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Algebra in the Stone-Cech Compactification by Neil Hindman,Dona Strauss Pdf

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Author : Leonard Gillman
Publisher : Courier Dover Publications
Page : 321 pages
File Size : 47,6 Mb
Release : 2018-01-16
Category : Mathematics
ISBN : 9780486816883

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Rings of Continuous Functions by Leonard Gillman Pdf

Designed as a text as well as a treatise, the first systematic account of the theory of rings of continuous functions remains the basic graduate-level book in this area. 1960 edition.

Author : Norman R. Howes
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208334

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Modern Analysis and Topology by Norman R. Howes Pdf

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.

Author : Richard Edward Chandler
Publisher : Unknown
Page : 172 pages
File Size : 46,7 Mb
Release : 1976
Category : Mathematics
ISBN : UOM:39015049381356

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Hausdorff Compactifications by Richard Edward Chandler Pdf

Author : Tai-Danae Bradley,Tyler Bryson,John Terilla
Publisher : MIT Press
Page : 167 pages
File Size : 45,7 Mb
Release : 2020-08-18
Category : Mathematics
ISBN : 9780262359627

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Topology by Tai-Danae Bradley,Tyler Bryson,John Terilla Pdf

A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.

Author : Volker Runde
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 41,9 Mb
Release : 2007-12-07
Category : Mathematics
ISBN : 038725790X

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A Taste of Topology by Volker Runde Pdf

This should be a revelation for mathematics undergraduates. Having evolved from Runde’s notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The well-chosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Runde’s text treats its material differently to other books on the subject, providing a fresh perspective.

Author : Aaron Robertson
Publisher : CRC Press
Page : 256 pages
File Size : 51,5 Mb
Release : 2021-06-17
Category : Mathematics
ISBN : 9780429775918

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Fundamentals of Ramsey Theory by Aaron Robertson Pdf

Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before. The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises. This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them. Additionally, the book offers: A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Čech compactification of the integers. A chapter on the probabilistic method since it is quite central to Ramsey-type numbers. A unique chapter presenting some applications of Ramsey theory. Exercises in every chapter The intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed. TABLE OF CONENTS Preface List of Figures List of Tables Symbols 1. Introduction 2. Integer Ramsey Theory 3. Graph Ramsey Theory 4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey Theory 6. The Probabilistic Method 7. Applications Bibliography Index Biography Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.

Author : Somashekhar Naimpally
Publisher : Walter de Gruyter
Page : 220 pages
File Size : 54,8 Mb
Release : 2010-10-01
Category : Mathematics
ISBN : 9783486598605

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Proximity Approach to Problems in Topology and Analysis by Somashekhar Naimpally Pdf

Dieses Buch konzentriert das aktuelle Gesamtwissen zum Proximity-Konzept und stellt es dem Leser in gut strukturierter Form dar. Hauptaugenmerk liegt auf den vielfältigen Möglichkeiten, die sich aus dem Proximity-Konzept der räumlichen Nähe und seiner Verallgemeinerung im Nearness-Konzept ergeben.

Author : H. J. Kowalsky
Publisher : Academic Press
Page : 297 pages
File Size : 43,9 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483265247

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Topological Spaces by H. J. Kowalsky Pdf

Topological Spaces focuses on the applications of the theory of topological spaces to the different branches of mathematics. The book first offers information on elementary principles, topological spaces, and compactness and connectedness. Discussions focus on locally compact spaces, local connectedness, fundamental concepts and their reformulations, lattice of topologies, axioms of separation, fundamental concepts of set theory, and ordered sets and lattices. The manuscript then ponders on mappings and extensions and characterization of topological spaces, including completely regular spaces, transference of topologies, Wallman compactification, and embeddings. The publication takes a look at metric and uniform spaces and applications of topological groups. Topics include the Stone-Weierstrass Approximation Theorem, extensions and completions of topological groups, topological rings and fields, extension and completion of uniform spaces, uniform continuity and uniform convergence, metric spaces, and metritization. The text is a valuable reference for mathematicians and researchers interested in the study of topological spaces.

Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 272 pages
File Size : 50,7 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9780486820804

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Category Theory in Context by Emily Riehl Pdf

Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Author : K. Kunen,J. Vaughan
Publisher : Elsevier
Page : 1282 pages
File Size : 48,9 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483295152

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Handbook of Set-Theoretic Topology by K. Kunen,J. Vaughan Pdf

This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest. In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.