Author: Neil Hindman
Publisher: Walter de Gruyter
ISBN: 3110258358
Category : Mathematics
Languages : en
Pages : 610
Book Description
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-Cech Compactification
Author: Neil Hindman
Publisher: Walter de Gruyter
ISBN: 3110258358
Category : Mathematics
Languages : en
Pages : 610
Book Description
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.
Publisher: Walter de Gruyter
ISBN: 3110258358
Category : Mathematics
Languages : en
Pages : 610
Book Description
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-Čech Compactification
Author: Neil Hindman
Publisher: Walter de Gruyter
ISBN: 9783110256239
Category : Mathematics
Languages : en
Pages : 591
Book Description
"The present book is the first devoted to an extensive study of the algebraic structure of betaS and the many applications thereof; it is an exciting book, written - and very well written - by two mathematicians who are eminently qualified two write it, and it is essentially self-contained, requiring only that the reader come to it with the basic concepts of first graduate courses in algebra, analysis and topology. [...] I recommend this book highly; it will be very useful, both to researchers and to students. ITs index, list of symbols and up-to-date bibliography are very helpful [...]."Paul Milnes, Zentralblatt MATH / 1998 "The authors present a self-contained exposition [...]. THe book under review is written by two mathematicians who have contributed in a decisive way to this rapidly expanding area [...] and provides a unique opportunity to obtain a 'colorful' panoramic view of the subject."Michael Tkacenko, MathSciNet / 1999
Publisher: Walter de Gruyter
ISBN: 9783110256239
Category : Mathematics
Languages : en
Pages : 591
Book Description
"The present book is the first devoted to an extensive study of the algebraic structure of betaS and the many applications thereof; it is an exciting book, written - and very well written - by two mathematicians who are eminently qualified two write it, and it is essentially self-contained, requiring only that the reader come to it with the basic concepts of first graduate courses in algebra, analysis and topology. [...] I recommend this book highly; it will be very useful, both to researchers and to students. ITs index, list of symbols and up-to-date bibliography are very helpful [...]."Paul Milnes, Zentralblatt MATH / 1998 "The authors present a self-contained exposition [...]. THe book under review is written by two mathematicians who have contributed in a decisive way to this rapidly expanding area [...] and provides a unique opportunity to obtain a 'colorful' panoramic view of the subject."Michael Tkacenko, MathSciNet / 1999
Algebra in the Stone-Čech Compactification
Author: Neil Hindman
Publisher: Walter de Gruyter
ISBN: 9783110154207
Category : Mathematics
Languages : en
Pages : 508
Book Description
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
Publisher: Walter de Gruyter
ISBN: 9783110154207
Category : Mathematics
Languages : en
Pages : 508
Book Description
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-Čech Compactification
Author: R.C. Walker
Publisher: Springer Science & Business Media
ISBN: 3642619355
Category : Science
Languages : en
Pages : 344
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 3642619355
Category : Science
Languages : en
Pages : 344
Book Description
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.
Algebra in the Stone-Cech Compactification
Author: Neil Hindman
Publisher: Walter de Gruyter
ISBN: 3110809222
Category : Mathematics
Languages : en
Pages : 501
Book Description
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
Publisher: Walter de Gruyter
ISBN: 3110809222
Category : Mathematics
Languages : en
Pages : 501
Book Description
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
Ergebnisse der Mathematik und ihrer Grenzgebiete
Author: Russell C. Walker
Publisher:
ISBN: 9780387066998
Category : Mathematics
Languages : en
Pages : 332
Book Description
Publisher:
ISBN: 9780387066998
Category : Mathematics
Languages : en
Pages : 332
Book Description
Rings of Continuous Functions
Author: Leonard Gillman
Publisher: Courier Dover Publications
ISBN: 0486816885
Category : Mathematics
Languages : en
Pages : 321
Book Description
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.
Publisher: Courier Dover Publications
ISBN: 0486816885
Category : Mathematics
Languages : en
Pages : 321
Book Description
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.
Spaces of Continuous Functions
Author: G.L.M. Groenewegen
Publisher: Springer
ISBN: 9462392013
Category : Mathematics
Languages : en
Pages : 173
Book Description
The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given.Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem.The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.
Publisher: Springer
ISBN: 9462392013
Category : Mathematics
Languages : en
Pages : 173
Book Description
The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given.Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem.The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.
An Invitation to General Algebra and Universal Constructions
Author: George M. Bergman
Publisher: Springer
ISBN: 3319114786
Category : Mathematics
Languages : en
Pages : 572
Book Description
Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
Publisher: Springer
ISBN: 3319114786
Category : Mathematics
Languages : en
Pages : 572
Book Description
Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
Category Theory in Context
Author: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Category : Mathematics
Languages : en
Pages : 272
Book Description
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.
Publisher: Courier Dover Publications
ISBN: 0486820807
Category : Mathematics
Languages : en
Pages : 272
Book Description
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.