Algebra In The Stone Cech Compactification
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Algebra In The Stone Cech Compactification
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Author : Neil Hindman
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-23
Algebra In The Stone Cech Compactification written by Neil Hindman and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Mathematics categories.
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.
Algebra In The Stone Ech Compactification
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Author : Neil Hindman
language : en
Publisher: Walter de Gruyter
Release Date : 1998
Algebra In The Stone Ech Compactification written by Neil Hindman and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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
The Stone Ech Compactification
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Author : R.C. Walker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Stone Ech Compactification written by R.C. Walker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete
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Author : Russell C. Walker
language : en
Publisher:
Release Date : 195?
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete written by Russell C. Walker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 195? with Mathematics categories.
Algebra In The Stone Cech Compactification
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Author : Neil Hindman
language : en
Publisher: Walter de Gruyter
Release Date : 2011-04-20
Algebra In The Stone Cech Compactification written by Neil Hindman and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-20 with Mathematics categories.
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
Tulane University Ring And Operator Theory Year 1970 1971
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Author : Karl H. Hofmann
language : en
Publisher: Springer
Release Date : 2006-11-15
Tulane University Ring And Operator Theory Year 1970 1971 written by Karl H. Hofmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Topological Algebras
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Author :
language : en
Publisher: Elsevier
Release Date : 2011-10-10
Topological Algebras written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-10 with Mathematics categories.
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–Čech compactification and the Wallman compactification play an important role in characterizing the maximal ideals of certain topological algebras.
Fundamentals Of Ramsey Theory
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Author : Aaron Robertson
language : en
Publisher: CRC Press
Release Date : 2021-06-17
Fundamentals Of Ramsey Theory written by Aaron Robertson and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-17 with Mathematics categories.
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.
A Taste Of Topology
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Author : Volker Runde
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-07
A Taste Of Topology written by Volker Runde and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-07 with Mathematics categories.
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.
Rings Of Continuous Functions
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Author : Leonard Gillman
language : en
Publisher: Courier Dover Publications
Release Date : 2018-01-16
Rings Of Continuous Functions written by Leonard Gillman and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-16 with Mathematics categories.
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.