Lectures on Boolean Algebras (eBook)

Paul R. Halmos (Autor)

eBook Download: EPUB

2018
160 Seiten
Dover Publications (Verlag)
978-0-486-83457-3 (ISBN)

Infos

Concise and informal as well as systematic, this presentation on the basics of Boolean algebra has ranked among the fundamental books on the subject since its initial publication in 1963.

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This presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise and informal as well as systematic, the text draws upon lectures delivered by Professor Halmos at the University of Chicago to cover many topics in brief individual chapters. The approach is suitable for advanced undergraduates and graduate students in mathematics.Starting with Boolean rings and algebras, the treatment examines fields of sets, regular open sets, elementary relations, infinite operations, subalgebras, homomorphisms, free algebras, ideals and filters, and the homomorphism theorem. Additional topics include measure algebras, Boolean spaces, the representation theorem, duality for ideals and for homomorphisms, Boolean measure spaces, isomorphisms of factors, projective and injective algebras, and many other subjects. Several chapters conclude with stimulating exercises; the solutions are not included.

Autor

Paul R. Halmos (1916–2006) was a prominent American mathematician who taught at the University of Chicago, the University of Michigan, and other schools and made significant contributions to several areas of mathematics, including mathematical logic, ergodic theory, functional analysis, and probability theory. His other Dover books are Algebraic Logic, Finite-Dimensional Vector Spaces, Introduction to Hilbert Space and the Theory of Spectral Multiplicity, Lectures on Ergodic Theory, and Naive Set Theory.

Inhalt

Preface 1. Boolean rings 2. Boolean algebras 3. Fields of sets 4. Regular open sets 5. Elementary relations 6. Order 7. Infinite operations 8. Subalgebras 9. Homomorphisms 10. Free algebras 11. Ideals and filters 12. The homomorphism theorem 13. Boolean o-algebras 14. The countable chain condition 15. Measure algebras 16. Atoms 17. Boolean spaces 18. The representation theorem 19. Duality for ideals 20. Duality for homomorphisms 21. Completion 22. Boolean o-spaces 23. The representation of o-algebras 24. Boolean measure spaces 25. Incomplete algebras 26. Products of algebras 27. Sums of algebras 28. Isomorphisms of factors 29. Isomorphisms of countable factors 30. Retracts 31. Projective algebras 32. Injective algebras Epilogue Index  

Produkt-Details

• Erscheint lt. Verlag: 12.9.2018
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• ISBN-10: 0-486-83457-3 / 0486834573
• ISBN-13: 978-0-486-83457-3 / 9780486834573