Continuous Lattices and Domains
Author: G. Gierz
Publisher: Cambridge University Press
Published: 2003-03-06
Total Pages: 640
ISBN-13: 9780521803380
DOWNLOAD EBOOK →Table of contents
Lanterna Rally
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Continuous Lattices
Author: B. Banaschewski
Publisher: Springer
Published: 2006-11-14
Total Pages: 428
ISBN-13: 3540387552
DOWNLOAD EBOOK →A Compendium of Continuous Lattices
Author: G. Gierz
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 390
ISBN-13: 3642676782
DOWNLOAD EBOOK →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.
Continuous Lattices and Their Applications
Author: Rudolf E. Hoffmann
Publisher: CRC Press
Published: 2020-12-17
Total Pages: 392
ISBN-13: 1000154173
DOWNLOAD EBOOK →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.
Continuous Lattices and Their Applications
Author: Rudolf E. Hoffmann
Publisher: CRC Press
Published: 2020-12-17
Total Pages: 392
ISBN-13: 1000111083
DOWNLOAD EBOOK →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.
Continuous Lattices and Related Topics
Author: Rudolf-Eberhard Hoffmann
Publisher:
Published: 1982
Total Pages: 330
ISBN-13:
DOWNLOAD EBOOK →The Shape of Congruence Lattices
Author: Keith Kearnes
Publisher: American Mathematical Soc.
Published: 2013-02-26
Total Pages: 183
ISBN-13: 0821883232
DOWNLOAD EBOOK →This monograph is concerned with the relationships between Maltsev conditions, commutator theories and the shapes of congruence lattices in varieties of algebras. The authors develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. They prove that a residually small variety that satisfies a congruence identity is congruence modular.
Ordered Sets and Lattices II
Author:
Publisher: American Mathematical Soc.
Published:
Total Pages: 262
ISBN-13: 9780821895887
DOWNLOAD EBOOK →This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.
Continuous Lattices
Author: B. Banaschewski
Publisher:
Published: 2014-09-01
Total Pages: 428
ISBN-13: 9783662197257
DOWNLOAD EBOOK →Computing the Continuous Discretely
Author: Matthias Beck
Publisher: Springer
Published: 2015-11-14
Total Pages: 295
ISBN-13: 1493929690
DOWNLOAD EBOOK →This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE
