Introduction to Boolean Algebras (eBook)

Steven Givant, Paul Halmos (Autoren)

eBook Download: PDF

2008 | 2009
XIV, 574 Seiten
Springer New York (Verlag)
978-0-387-68436-9 (ISBN)

Infos

This book is an informal though systematic series of lectures on Boolean algebras. It contains background chapters on topology and continuous functions and includes hundreds of exercises as well as a solutions manual.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 10.12.2008
• Reihe/Serie: Undergraduate Texts in Mathematics
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Technik
• Schlagworte: Algebra • Boolean algebra • Division • Homomorphism • lattice • set theory
• ISBN-10: 0-387-68436-0 / 0387684360
• ISBN-13: 978-0-387-68436-9 / 9780387684369