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Ordered Groups And Topology
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Book Synopsis Ordered Groups and Topology by : Adam J. Clay
Download or read book Ordered Groups and Topology written by Adam J. Clay and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book w.
Book Synopsis Ordered Groups and Topology by : Adam Clay
Download or read book Ordered Groups and Topology written by Adam Clay and published by American Mathematical Soc.. This book was released on 2016-11-16 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
Book Synopsis Lattice-Ordered Groups by : M.E Anderson
Download or read book Lattice-Ordered Groups written by M.E Anderson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].
Book Synopsis Topology and Order by : Leopoldo Nachbin
Download or read book Topology and Order written by Leopoldo Nachbin and published by . This book was released on 1965 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Topics on Representations of Ordered Structures and Utility Theory by : Gianni Bosi
Download or read book Mathematical Topics on Representations of Ordered Structures and Utility Theory written by Gianni Bosi and published by Springer Nature. This book was released on 2020-01-23 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an essential review of central theories, current research and applications in the field of numerical representations of ordered structures. It is intended as a tribute to Professor Ghanshyam B. Mehta, one of the leading specialists on the numerical representability of ordered structures, and covers related applications to utility theory, mathematical economics, social choice theory and decision-making. Taken together, the carefully selected contributions provide readers with an authoritative review of this research field, as well as the knowledge they need to apply the theories and methods in their own work.
Book Synopsis Orderable Groups by : Roberta Botto Mura
Download or read book Orderable Groups written by Roberta Botto Mura and published by . This book was released on 1977 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Theory of Lattice-Ordered Groups by : V.M. Kopytov
Download or read book The Theory of Lattice-Ordered Groups written by V.M. Kopytov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way. These connections were established in the period between the end of 19th and beginning of 20th century. It was realized that ordered algebraic systems occur in various branches of mathemat ics bound up with its fundamentals. For example, the classification of infinitesimals resulted in discovery of non-archimedean ordered al gebraic systems, the formalization of the notion of real number led to the definition of ordered groups and ordered fields, the construc tion of non-archimedean geometries brought about the investigation of non-archimedean ordered groups and fields. The theory of partially ordered groups was developed by: R. Dedekind, a. Holder, D. Gilbert, B. Neumann, A. I. Mal'cev, P. Hall, G. Birkhoff. These connections between partial order and group operations allow us to investigate the properties of partially ordered groups. For exam ple, partially ordered groups with interpolation property were intro duced in F. Riesz's fundamental paper [1] as a key to his investigations of partially ordered real vector spaces, and the study of ordered vector spaces with interpolation properties were continued by many functional analysts since. The deepest and most developed part of the theory of partially ordered groups is the theory of lattice-ordered groups. In the 40s, following the publications of the works by G. Birkhoff, H. Nakano and P.
Download or read book Ordered Sets written by Bernd Schröder and published by Birkhäuser. This book was released on 2016-05-11 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.
Book Synopsis Introduction to Topological Groups by : Taqdir Husain
Download or read book Introduction to Topological Groups written by Taqdir Husain and published by Courier Dover Publications. This book was released on 2018-02-15 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.
Book Synopsis Topological Lattice Ordered Groups by : Robert Lewis Madell
Download or read book Topological Lattice Ordered Groups written by Robert Lewis Madell and published by . This book was released on 1968 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lattice-Ordered Groups by : A.M. Glass
Download or read book Lattice-Ordered Groups written by A.M. Glass and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lattice-ordered group is a mathematical structure combining a (partial) order (lattice) structure and a group structure (on a set) in a compatible way. Thus it is a composite structure, or, a set carrying two or more simple structures in a compatible way. The field of lattice-ordered groups turn up on a wide range of mathematical fields ranging from functional analysis to universal algebra. These papers address various aspects of the field, with wide applicability for interested researchers.
Book Synopsis A Concise Course in Algebraic Topology by : J. P. May
Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Book Synopsis Theory of Lattice-Ordered Groups by : Michael Darnel
Download or read book Theory of Lattice-Ordered Groups written by Michael Darnel and published by CRC Press. This book was released on 2021-12-16 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a thorough discussion of the orderability of a group. The book details the major developments in the theory of lattice-ordered groups, delineating standard approaches to structural and permutation representations. A radically new presentation of the theory of varieties of lattice-ordered groups is offered.;This work is intended for pure and applied mathematicians and algebraists interested in topics such as group, order, number and lattice theory, universal algebra, and representation theory; and upper-level undergraduate and graduate students in these disciplines.;College or university bookstores may order five or more copies at a special student price which is available from Marcel Dekker Inc, upon request.
Book Synopsis Ordered Groups and Infinite Permutation Groups by : W.C. Holland
Download or read book Ordered Groups and Infinite Permutation Groups written by W.C. Holland and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subjects of ordered groups and of infinite permutation groups have long en joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that time, both P. Conrad and P. Cohn had showed that a group admits a total right ordering if and only if the group is a group of automor phisms of a totally ordered set. (In a right ordered group, the order is required to be preserved by all right translations, unlike a (two-sided) ordered group, where both right and left translations must preserve the order.
Book Synopsis Partially Ordered Abelian Groups with Interpolation by : Kenneth R. Goodearl
Download or read book Partially Ordered Abelian Groups with Interpolation written by Kenneth R. Goodearl and published by American Mathematical Soc.. This book was released on 2010 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: A branch of ordered algebraic structures has grown, motivated by $K$-theoretic applications and mainly concerned with partially ordered abelian groups satisfying the Riesz interpolation property. This monograph is the first source in which the algebraic and analytic aspects of these interpolation groups have been integrated into a coherent framework for general reference. The author provides a solid foundation in the structure theory of interpolation groups and dimension groups (directed unperforated interpolation groups), with applications to ordered $K$-theory particularly in mind. Although interpolation groups are defined as purely algebraic structures, their development has been strongly influenced by functional analysis. This cross-cultural development has left interpolation groups somewhat estranged from both the algebraists, who may feel intimidated by compact convex sets, and the functional analysts, who may feel handicapped by the lack of scalars. This book, requiring only standard first-year graduate courses in algebra and functional analysis, aims to make the subject accessible to readers from both disciplines. High points of the development include the following: characterization of dimension groups as direct limits of finite products of copies of the integers; the double-dual representation of an interpolation group with order-unit via affine continuous real-valued functions on its state space; the structure of dimension groups complete with respect to the order-unit norm, as well as monotone sigma-complete dimension groups and dimension groups with countably infinite interpolation; and an introduction to the problem of classifying extensions of one dimension group by another. The book also includes a development of portions of the theory of compact convex sets and Choquet simplices, and an expository discussion of various applications of interpolation group theory to rings and $C^*$-algebras via ordered $K_0$. A discussion of some open problems in interpolation groups and dimension groups concludes the book. Of interest, of course, to researchers in ordered algebraic structures, the book will also be a valuable source for researchers seeking a background in interpolation groups and dimension groups for applications to such subjects as rings, operator algebras, topological Markov chains, positive polynomials, compact group actions, or other areas where ordered Grothendieck groups might be useful. This is a reprint of the 1986 original. (SURV/20.S)
Book Synopsis Ordered Algebraic Structures by : Jorge Martínez
Download or read book Ordered Algebraic Structures written by Jorge Martínez and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the 28th of February through the 3rd of March, 2001, the Department of Math ematics of the University of Florida hosted a conference on the many aspects of the field of Ordered Algebraic Structures. Officially, the title was "Conference on Lattice Ordered Groups and I-Rings", but its subject matter evolved beyond the limitations one might associate with such a label. This volume is officially the proceedings of that conference, although, likewise, it is more accurate to view it as a complement to that event. The conference was the fourth in wh at has turned into aseries of similar conferences, on Ordered Algebraic Structures, held in consecutive years. The first, held at the University of Florida in Spring, 1998, was a modest and informal affair. The fifth is in the final planning stages at this writing, for March 7-9, 2002, at Vanderbilt University. And although these events remain modest and reasonably informal, their scope has broadened, as they have succeeded in attracting mathematicians from other, related fields, as weIl as from more distant lands.
Author :O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov Publisher :American Mathematical Soc. ISBN 13 :9780821886250 Total Pages :432 pages Book Rating :4.8/5 (862 download)
Book Synopsis Elementary Topology by : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Download or read book Elementary Topology written by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov and published by American Mathematical Soc.. This book was released on with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.
