Introduction to Boolean Algebras
A special feature of the book is the large number of exercises of varying levels of difficulty, from routine problems that help readers understand the basic definitions and theorems, to intermediate problems that extend or enrich material developed in the text, to harder problems that explore import...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2009, 2009
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| Edition: | 1st ed. 2009 |
| Series: | Undergraduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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