Ultrafilters and Topologies on Groups

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Publisher : Walter de Gruyter
ISBN 13 : 3110213222
Total Pages : 229 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Ultrafilters and Topologies on Groups by : Yevhen Zelenyuk

Download or read book Ultrafilters and Topologies on Groups written by Yevhen Zelenyuk and published by Walter de Gruyter. This book was released on 2011-03-29 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the relationship between ultrafilters and topologies on groups. It shows how ultrafilters are used in constructing topologies on groups with extremal properties and how topologies on groups serve in deriving algebraic results about ultrafilters. The contents of the book fall naturally into three parts. The first, comprising Chapters 1 through 5, introduces to topological groups and ultrafilters insofar as the semigroup operation on ultrafilters is not required. Constructions of some important topological groups are given. In particular, that of an extremally disconnected topological group based on a Ramsey ultrafilter. Also one shows that every infinite group admits a nondiscrete zero-dimensional topology in which all translations and the inversion are continuous. In the second part, Chapters 6 through 9, the Stone-Cêch compactification βG of a discrete group G is studied. For this, a special technique based on the concepts of a local left group and a local homomorphism is developed. One proves that if G is a countable torsion free group, then βG contains no nontrivial finite groups. Also the ideal structure of βG is investigated. In particular, one shows that for every infinite Abelian group G, βG contains 22|G| minimal right ideals. In the third part, using the semigroup βG, almost maximal topological and left topological groups are constructed and their ultrafilter semigroups are examined. Projectives in the category of finite semigroups are characterized. Also one shows that every infinite Abelian group with finitely many elements of order 2 is absolutely ω-resolvable, and consequently, can be partitioned into ω subsets such that every coset modulo infinite subgroup meets each subset of the partition. The book concludes with a list of open problems in the field. Some familiarity with set theory, algebra and topology is presupposed. But in general, the book is almost self-contained. It is aimed at graduate students and researchers working in topological algebra and adjacent areas.

Ultrafilters and Topologies on Groups

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Publisher :
ISBN 13 : 9789667148140
Total Pages : 258 pages
Book Rating : 4.1/5 (481 download)

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Book Synopsis Ultrafilters and Topologies on Groups by : Mahmoud Filali

Download or read book Ultrafilters and Topologies on Groups written by Mahmoud Filali and published by . This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Progress in General Topology II

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Publisher : Elsevier
ISBN 13 : 0080929958
Total Pages : 651 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Recent Progress in General Topology II by : M. Husek

Download or read book Recent Progress in General Topology II written by M. Husek and published by Elsevier. This book was released on 2002-11-13 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents surveys describing recent developments in most of the primary subfields ofGeneral Topology and its applications to Algebra and Analysis during the last decade. It follows freelythe previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared inconnection with the Prague Topological Symposium, held in 2001. During the last 10 years the focusin General Topology changed and therefore the selection of topics differs slightly from thosechosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (includingInfinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic could be included in this book. Except surveys, the book contains several historical essays written by such eminent topologists as:R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added. List of all authors of surveys: A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.

Algebra in the Stone-Cech Compactification

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Publisher : Walter de Gruyter
ISBN 13 : 3110258358
Total Pages : 610 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Algebra in the Stone-Cech Compactification by : Neil Hindman

Download or read book Algebra in the Stone-Cech Compactification written by Neil Hindman and published by Walter de Gruyter. This book was released on 2011-12-23 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topological Algebras and their Applications

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110413558
Total Pages : 317 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Topological Algebras and their Applications by : Alexander Katz

Download or read book Topological Algebras and their Applications written by Alexander Katz and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-05-07 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the 8th International Conference of Topological Algebras and Their Applications (ICTAA-2014), held on May 26-30, 2014 in Playa de Villas de Mar Beach, dedicated to the memory of Anastasios Mallios (Athens, Greece). This series of conferences started in 1999 in Tartu, Estonia and were subsequently held in Rabat, Moroco (2000), Oulu, Finland (2001), Oaxaca, Mexico (2002), Bedlewo, Poland (2003), Athens, Greece (2005) and Tartu, Estonia (2008 and 2013). The topics of the conference include all areas of mathematics, connected with (preferably general) topological algebras and their applications, including all kinds of topological-algebraic structures as topological linear spaces, topological rings, topological modules, topological groups and semigroups; bornological-algebraic structures such as bornological linear spaces, bornological algebras, bornological groups, bornological rings and modules; algebraic and topological K-theory; topological module bundles, sheaves and others. Contents Some results on spectral properties of unital algebras and on the algebra of linear operators on a unital algebra Descriptions of all closed maximal one-sided ideals in topological algebras On non self-adjoint operators defined by Riesz bases in Hilbert and rigged Hilbert spaces Functional calculus on algebras of operators generated by a self-adjoint operator in Pontryagin space Π1 On Gelfand-Naimark type Theorems for unital abelian complex and real locally C*-, and locally JB-algebras Multipliers and strictly real topological algebras Multipliers in some perfect locally m-pseudo-convex algebras Wedderburn structure theorems for two-sided locally m-convex H*-algebras Homologically best modules in classical and quantized functional analysis Operator Grüss inequality Main embedding theorems for symmetric spaces of measurable functions Mapping class groups are linear Subnormable A-convex algebras Commutative BP*-algebras and Gelfand-Naimark’s theorem Discrete nonclosed subsets in maximally nondiscrete topological groups Faithfully representable topological *-algebras: some spectral properties On continuity of complementors in topological algebras Dominated ergodic theorem for isometries of non-commutative Lp-spaces, 1 p p ≠ 2 Ranks and the approximate n-th root property of C*-algebras Dense ideals in topological algebras: some results and open problems

Open Problems in Topology II

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Publisher : Elsevier
ISBN 13 : 9780080475295
Total Pages : 776 pages
Book Rating : 4.4/5 (752 download)

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Book Synopsis Open Problems in Topology II by : Elliott M. Pearl

Download or read book Open Problems in Topology II written by Elliott M. Pearl and published by Elsevier. This book was released on 2011-08-11 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world

The Theory of Ultrafilters

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Publisher : Springer
ISBN 13 :
Total Pages : 518 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Theory of Ultrafilters by : William Wistar Comfort

Download or read book The Theory of Ultrafilters written by William Wistar Comfort and published by Springer. This book was released on 1974 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: An ultrafilter is a truth-value assignment to the family of subsets of a set, and a method of convergence to infinity. From the first (logical) property arises its connection with two-valued logic and model theory; from the second (convergence) property arises its connection with topology and set theory. Both these descriptions of an ultrafilter are connected with compactness. The model-theoretic property finds its expression in the construction of the ultraproduct and the compactness type of theorem of Los (implying the compactness theorem of first-order logic); and the convergence property leads to the process of completion by the adjunction of an ideal element for every ultrafilter-i. e., to the Stone-Cech com- pactification process (implying the Tychonoff theorem on the compact- ness of products). Since these are two ways of describing the same mathematical object, it is reasonable to expect that a study of ultrafilters from these points of view will yield results and methods which can be fruitfully crossbred. This unifying aspect is indeed what we have attempted to emphasize in the present work.

Handbook of Set-Theoretic Topology

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Publisher : Elsevier
ISBN 13 : 148329515X
Total Pages : 1282 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Handbook of Set-Theoretic Topology by : K. Kunen

Download or read book Handbook of Set-Theoretic Topology written by K. Kunen and published by Elsevier. This book was released on 2014-06-28 with total page 1282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topological Groups and Related Structures, An Introduction to Topological Algebra.

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Publisher : Springer Science & Business Media
ISBN 13 : 949121635X
Total Pages : 794 pages
Book Rating : 4.4/5 (912 download)

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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 and published by Springer Science & Business Media. This book was released on 2008-05-01 with total page 794 pages. 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.

Topological Groups

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Publisher : MDPI
ISBN 13 : 303897644X
Total Pages : 160 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis Topological Groups by : Sidney A. Morris

Download or read book Topological Groups written by Sidney A. Morris and published by MDPI. This book was released on 2019-03-05 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the tremendous reception of our first volume on topological groups called "Topological Groups: Yesterday, Today, and Tomorrow", we now present our second volume. Like the first volume, this collection contains articles by some of the best scholars in the world on topological groups. A feature of the first volume was surveys, and we continue that tradition in this volume with three new surveys. These surveys are of interest not only to the expert but also to those who are less experienced. Particularly exciting to active researchers, especially young researchers, is the inclusion of over three dozen open questions. This volume consists of 11 papers containing many new and interesting results and examples across the spectrum of topological group theory and related topics. Well-known researchers who contributed to this volume include Taras Banakh, Michael Megrelishvili, Sidney A. Morris, Saharon Shelah, George A. Willis, O'lga V. Sipacheva, and Stephen Wagner.

Topologies on Groups Determined by Sequences

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Publisher :
ISBN 13 :
Total Pages : 114 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Topologies on Groups Determined by Sequences by : Ihor Protasov

Download or read book Topologies on Groups Determined by Sequences written by Ihor Protasov and published by . This book was released on 1999 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ultrafilters and Topologies

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ISBN 13 : 9781374739437
Total Pages : pages
Book Rating : 4.7/5 (394 download)

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Book Synopsis Ultrafilters and Topologies by : 黃毅英

Download or read book Ultrafilters and Topologies written by 黃毅英 and published by . This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Structure and Regularity of Group Actions on One-Manifolds

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Publisher : Springer Nature
ISBN 13 : 3030890066
Total Pages : 323 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Structure and Regularity of Group Actions on One-Manifolds by : Sang-hyun Kim

Download or read book Structure and Regularity of Group Actions on One-Manifolds written by Sang-hyun Kim and published by Springer Nature. This book was released on 2021-11-19 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of optimal and critical regularities of groups of diffeomorphisms, from the classical work of Denjoy and Herman, up through recent advances. Beginning with an investigation of regularity phenomena for single diffeomorphisms, the book goes on to describes a circle of ideas surrounding Filipkiewicz's Theorem, which recovers the smooth structure of a manifold from its full diffeomorphism group. Topics covered include the simplicity of homeomorphism groups, differentiability of continuous Lie group actions, smooth conjugation of diffeomorphism groups, and the reconstruction of spaces from group actions. Various classical and modern tools are developed for controlling the dynamics of general finitely generated group actions on one-dimensional manifolds, subject to regularity bounds, including material on Thompson's group F, nilpotent groups, right-angled Artin groups, chain groups, finitely generated groups with prescribed critical regularities, and applications to foliation theory and the study of mapping class groups. The book will be of interest to researchers in geometric group theory.

Pseudocompact Topological Spaces

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Publisher : Springer
ISBN 13 : 3319916807
Total Pages : 299 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Pseudocompact Topological Spaces by : Michael Hrušák

Download or read book Pseudocompact Topological Spaces written by Michael Hrušák and published by Springer. This book was released on 2018-07-19 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, intended for postgraduate students and researchers, presents many results of historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of pseudocompactness which generalizes a property of compact subsets of the real line. A topological space is pseudocompact if the range of any real-valued, continuous function defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures. The collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. In addition, the text examines new lines of research that have been at the forefront of mathematics. There is, as yet, no text that systematically compiles and develops the extensive theory of pseudocompact spaces, making this book an essential asset for anyone in the field of topology.

Mathematical Reviews

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ISBN 13 :
Total Pages : 840 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 840 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ultrafilters and Topologies

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ISBN 13 :
Total Pages : 114 pages
Book Rating : 4.:/5 (52 download)

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Book Synopsis Ultrafilters and Topologies by : Ngai-ying Wong

Download or read book Ultrafilters and Topologies written by Ngai-ying Wong and published by . This book was released on 1981 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Siberian Mathematical Journal

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Publisher :
ISBN 13 :
Total Pages : 648 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Siberian Mathematical Journal by :

Download or read book Siberian Mathematical Journal written by and published by . This book was released on 1993 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: