Introduction to Boolean algebras

This book is an informal, although systematic presentation of lectures given by the authors on Boolean algebras, intended for advanced undergraduates and beginning graduate students. In a bold and refreshing style, this book treats Boolean algebras, develops some intriguing ideas, and provides rare insights. Exercises are generously sprinkled throughout the text for course study. This book can be considered a sequel to Paul Halmos's Lectures on Boolean Algebras, with the following changes: (1) the material in every section has been explained in more detail, and is now more accessible to undergraduates; (2) there arethree times as many exercises, and the authors have now prepared a solutions manual; (3) a more careful explanation of the relationship between Boolean rings and Boolean algebras has been added; (4) thirteen chapters have been added,including chapters on topology and on continuous functions, a chapter on the extension theorem for homomorphisms. Provides a friendly introduction to Boolean algebras Includes hundres of exercises and a solutions manual Contains background chapters on topology and continuous functions Author has streamlined many of the proofs and rearranged material in a more logical order INDICE: From the contents Boolean Rings.- Boolean Algebras.- Boolean Algebras versus Rings.- The Principle of Duality.- Fieldsandnbsp;of Sets.- Elementary Relations.- Order.- Infinite Operations.- Topology.- Regular Open Sets.- Subalgebras.- Homomorphisms.- Extensions of Homomorphisms.- Atoms.- Finite Boolean Algebras.- Atomless Boolean Algebras.- Congruences and Quotients.- Ideals and Filters.- Lattices of Ideals.- Maximal Ideals.- Homomorphism and Isomorphism Theorems.- The Representation Theorem.- Canonical Extensions.- Complete Homomorphisms and Complete Ideals.- Completions.- Products of Algebras.- Isomorphisms of Factors.- Free Algebras.- Boolean o-algebras.- The Countable Chain Condition.- Measure Algebras.- Boolean Spaces.- Continuous Functions.- Boolean Algebras and Boolean Spaces.- Duality for Ideals.- Duality for Homomorphisms.-Duality for Subalgebras.- Dualtiy for Completeness.- Boolean o-spaces.- The Representation of o-algebras.- Boolean Measure Spaces.- Incomplete Algebras.- Dualtiy for Products.

• ISBN: 978-0-387-40293-2
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 585
• Fecha Publicación: 01/01/2009
• Nº Volúmenes: 1
• Idioma: Inglés