Handbook of Boolean Algebras
Author : Sabine Koppelberg
Publisher :
Page : 312 pages
File Size : 15,1 MB
Release : 1989
Category : Algebra, Boolean
ISBN : 9780444872913
Author : Sabine Koppelberg
Publisher :
Page : 312 pages
File Size : 15,1 MB
Release : 1989
Category : Algebra, Boolean
ISBN : 9780444872913
Author : Sabine Koppelberg
Publisher : North Holland
Page : 370 pages
File Size : 43,47 MB
Release : 1989
Category : Mathematics
ISBN :
Author : J. Donald Monk
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 24,20 MB
Release : 2010-03-25
Category : Mathematics
ISBN : 3034603347
This text covers cardinal number valued functions defined for any Boolean algebra such as cellularity. It explores the behavior of these functions under algebraic operations such as products, free products, ultraproducts and their relationships to each other.
Author :
Publisher :
Page : pages
File Size : 38,12 MB
Release : 1989
Category :
ISBN :
Author : J. Donald Monk
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 31,15 MB
Release : 2014-02-11
Category : Mathematics
ISBN : 3034807309
This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of the earlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping number. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including interval algebras, tree algebras and superatomic algebras.
Author : Charles C Pinter
Publisher : Courier Corporation
Page : 402 pages
File Size : 49,9 MB
Release : 2010-01-14
Category : Mathematics
ISBN : 0486474178
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Author : Granino A. Korn
Publisher : Courier Corporation
Page : 1154 pages
File Size : 45,69 MB
Release : 2013-04-26
Category : Technology & Engineering
ISBN : 0486320235
Convenient access to information from every area of mathematics: Fourier transforms, Z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, game theory, much more.
Author : D.A. Vladimirov
Publisher : Springer Science & Business Media
Page : 614 pages
File Size : 15,24 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 940170936X
Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting classical theorems, the book describes the topologies and uniform structures of Boolean algebras, the basics of complete Boolean algebras and their continuous homomorphisms, as well as lifting theory. The first part also includes an introductory chapter describing the elementary to the theory. The second part deals at a graduate level with the metric theory of Boolean algebras at a graduate level. The covered topics include measure algebras, their sub algebras, and groups of automorphisms. Ample room is allotted to the new classification theorems abstracting the celebrated counterparts by D.Maharam, A.H. Kolmogorov, and V.A.Rokhlin. Boolean Algebras in Analysis is an exceptional definitive source on Boolean algebra as applied to functional analysis and probability. It is intended for all who are interested in new and powerful tools for hard and soft mathematical analysis.
Author : Marco Aiello
Publisher : Springer Science & Business Media
Page : 1072 pages
File Size : 12,3 MB
Release : 2007-09-04
Category : Science
ISBN : 1402055870
The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject.
Author : Eric Schechter
Publisher : Academic Press
Page : 907 pages
File Size : 35,13 MB
Release : 1996-10-24
Category : Mathematics
ISBN : 0080532993
Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/