Introduction to Boolean Algebras

• Main Authors: Halmos, Paul (Author), Givant, Steven (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Algebra.; Ordered algebraic structures.; Mathematical logic.; Mathematical Logic and Foundations.; Order, Lattices, Ordered Algebraic Structures.

In a bold and refreshingly informal style, this exciting text steers a middle course between elementary texts emphasizing connections with philosophy, logic, and electronic circuit design, and profound treatises aimed at advanced graduate students and professional mathematicians. It is written for r...

Table of Contents:

• Boolean Rings
• Boolean Algebras
• Boolean Algebras Versus Rings
• The Principle of Duality
• Fields 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 s-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
• Duality for Completeness
• Boolean s-spaces
• The Representation of s-algebras
• Boolean Measure Spaces
• Incomplete Algebras
• Duality for Products
• Sums of Algebras
• Isomorphisms of Countable Factors.