Representations Of Distributive Topological Lattices Of Finite Breadth
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Author |
: Henry Forrest Bunch |
Publisher |
: |
Total Pages |
: 144 |
Release |
: 1981 |
ISBN-10 |
: UCR:31210006667859 |
ISBN-13 |
: |
Rating |
: 4/5 (59 Downloads) |
Synopsis Representations of Distributive Topological Lattices of Finite Breadth by : Henry Forrest Bunch
Author |
: Damon Lucifer Ellingston |
Publisher |
: |
Total Pages |
: 74 |
Release |
: 1990 |
ISBN-10 |
: OCLC:22233911 |
ISBN-13 |
: |
Rating |
: 4/5 (11 Downloads) |
Synopsis Representations in Topology of Distributive Lattices by : Damon Lucifer Ellingston
Author |
: Raymond Balbes |
Publisher |
: Ray Balbes |
Total Pages |
: 320 |
Release |
: 1975 |
ISBN-10 |
: UOM:39015014356821 |
ISBN-13 |
: |
Rating |
: 4/5 (21 Downloads) |
Synopsis Distributive Lattices by : Raymond Balbes
Author |
: George Grätzer |
Publisher |
: Springer Nature |
Total Pages |
: 440 |
Release |
: 2023-03-23 |
ISBN-10 |
: 9783031290633 |
ISBN-13 |
: 3031290631 |
Rating |
: 4/5 (33 Downloads) |
Synopsis The Congruences of a Finite Lattice by : George Grätzer
The congruences of a lattice form the congruence lattice. Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems. Written by one of the leading experts in lattice theory, this text provides a self-contained introduction to congruences of finite lattices and presents the major results of the last 90 years. It features the author’s signature “Proof-by-Picture” method, which is used to convey the ideas behind formal proofs in a visual, more intuitive manner. Key features include: an insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions complete proofs, an extensive bibliography and index, and over 180 illustrations additional chapters covering new results of the last seven years, increasing the size of this edition to 430 pages, 360 statements, and 262 references This text is appropriate for a one-semester graduate course in lattice theory, and it will also serve as a valuable reference for researchers studying lattices. Reviews of previous editions: “[This] monograph...is an exceptional work in lattice theory, like all the contributions by this author. The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory. — Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica LII (1), 2007 "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasis on the more 'geometric' aspects." — Mathematical Reviews
Author |
: Mai Gehrke |
Publisher |
: Cambridge University Press |
Total Pages |
: 369 |
Release |
: 2024-02-29 |
ISBN-10 |
: 9781009349697 |
ISBN-13 |
: 1009349694 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Topological Duality for Distributive Lattices by : Mai Gehrke
Introducing Stone-Priestley duality theory and its applications to logic and theoretical computer science, this book equips graduate students and researchers with the theoretical background necessary for reading and understanding current research in the area. After giving a thorough introduction to the algebraic, topological, logical, and categorical aspects of the theory, the book covers two advanced applications in computer science, namely in domain theory and automata theory. These topics are at the forefront of active research seeking to unify semantic methods with more algorithmic topics in finite model theory. Frequent exercises punctuate the text, with hints and references provided.
Author |
: Alan Joregon Burger |
Publisher |
: |
Total Pages |
: 144 |
Release |
: 1975 |
ISBN-10 |
: OCLC:6240367 |
ISBN-13 |
: |
Rating |
: 4/5 (67 Downloads) |
Synopsis Contributions to the Topological Representation of Bounded Distributive Lattices by : Alan Joregon Burger
Author |
: Steven Roman |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 307 |
Release |
: 2008-12-15 |
ISBN-10 |
: 9780387789019 |
ISBN-13 |
: 0387789014 |
Rating |
: 4/5 (19 Downloads) |
Synopsis Lattices and Ordered Sets by : Steven Roman
This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. Lattice theory began in the early 1890s, when Richard Dedekind wanted to know the answer to the following question: Given three subgroups EF , and G of an abelian group K, what is the largest number of distinct subgroups that can be formed using these subgroups and the operations of intersection and sum (join), as in E?FßÐE?FÑ?GßE?ÐF?GÑ and so on? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann.
Author |
: G. Gierz |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 390 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642676789 |
ISBN-13 |
: 3642676782 |
Rating |
: 4/5 (89 Downloads) |
Synopsis A Compendium of Continuous Lattices by : G. Gierz
A mathematics book with six authors is perhaps a rare enough occurrence to make a reader ask how such a collaboration came about. We begin, therefore, with a few words on how we were brought to the subject over a ten-year period, during part of which time we did not all know each other. We do not intend to write here the history of continuous lattices but rather to explain our own personal involvement. History in a more proper sense is provided by the bibliography and the notes following the sections of the book, as well as by many remarks in the text. A coherent discussion of the content and motivation of the whole study is reserved for the introduction. In October of 1969 Dana Scott was lead by problems of semantics for computer languages to consider more closely partially ordered structures of function spaces. The idea of using partial orderings to correspond to spaces of partially defined functions and functionals had appeared several times earlier in recursive function theory; however, there had not been very sustained interest in structures of continuous functionals. These were the ones Scott saw that he needed. His first insight was to see that - in more modern terminology - the category of algebraic lattices and the (so-called) Scott-continuous functions is cartesian closed.
Author |
: Siemion Fajtlowicz |
Publisher |
: |
Total Pages |
: 692 |
Release |
: 1973 |
ISBN-10 |
: UOM:39015017310312 |
ISBN-13 |
: |
Rating |
: 4/5 (12 Downloads) |
Synopsis Proceedings of the University of Houston Lattice Theory Conference, March 22-24, 1973 by : Siemion Fajtlowicz
Author |
: Ralph S. Freese |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 304 |
Release |
: 1995 |
ISBN-10 |
: 9780821803899 |
ISBN-13 |
: 0821803891 |
Rating |
: 4/5 (99 Downloads) |
Synopsis Free Lattices by : Ralph S. Freese
A thorough treatment of free lattices, including such aspects as Whitman's solution to the word problem, bounded monomorphisms and related concepts, totally atomic elements, infinite intervals, computation, term rewrite systems, and varieties. Includes several results that are new or have not been previously published. Annotation copyright by Book News, Inc., Portland, OR