Topological Duality For Distributive Lattices

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Topological Duality For Distributive Lattices

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Author : Mai Gehrke
language : en
Publisher: Cambridge University Press
Release Date : 2024-02-29

Topological Duality For Distributive Lattices written by Mai Gehrke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-29 with Computers categories.

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.

Topological Duality For Distributive Lattices

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Author : Mai Gehrke
language : en
Publisher: Cambridge University Press
Release Date : 2024-02-29

Topological Duality For Distributive Lattices written by Mai Gehrke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-29 with Computers categories.

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.

Lattice Theory

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Author : George Gratzer
language : en
Publisher: Courier Corporation
Release Date : 2009-01-01

Lattice Theory written by George Gratzer and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Mathematics categories.

This outstanding text is written in clear language and enhanced with many exercises, diagrams, and proofs. It discusses historical developments and future directions and provides an extensive bibliography and references. 1971 edition.

Continuous Lattices And Their Applications

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Author : Rudolf E. Hoffmann
language : en
Publisher: CRC Press
Release Date : 2020-12-17

Continuous Lattices And Their Applications written by Rudolf E. Hoffmann and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Computers categories.

This book contains articles on the notion of a continuous lattice, which has its roots in Dana Scott's work on a mathematical theory of computation, presented at a conference on categorical and topological aspects of continuous lattices held in 1982.

Distributive Lattices And Their Applications In Complex Analysis

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Author : Viktor Viktorovich Zharinov
language : en
Publisher: American Mathematical Soc.
Release Date : 1985

Distributive Lattices And Their Applications In Complex Analysis written by Viktor Viktorovich Zharinov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.

Algebraic methods have penetrated deeply into contemporary complex analysis, having an essential influence on both the choice of problems and on the methods for solving them. This monograph deals with the applications of distributive lattices of subspaces to problems in multidimensional complex analysis.

Distributive Lattices

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Author : Raymond Balbes
language : en
Publisher: Ray Balbes
Release Date : 1975

Distributive Lattices written by Raymond Balbes and has been published by Ray Balbes this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.

Continuous Lattices And Domains

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Author : G. Gierz
language : en
Publisher: Cambridge University Press
Release Date : 2003-03-06

Continuous Lattices And Domains written by G. Gierz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-06 with Mathematics categories.

Table of contents

A Compendium Of Continuous Lattices

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Author : G. Gierz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

A Compendium Of Continuous Lattices written by G. Gierz 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 Mathematics categories.

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.

The Pontryagin Duality Of Compact O Dimensional Semilattices And Its Applications

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Author : K.H. Hofmann
language : en
Publisher: Springer
Release Date : 2006-11-15

The Pontryagin Duality Of Compact O Dimensional Semilattices And Its Applications written by K.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.

Lattices And Ordered Sets

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Author : Steven Roman
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15

Lattices And Ordered Sets written by Steven Roman 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 2008-12-15 with Mathematics categories.

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.