Lectures on Boolean Algebras
eBook - ePub

Lectures on Boolean Algebras

  1. 160 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Lectures on Boolean Algebras

About this book

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.

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Yes, you can access Lectures on Boolean Algebras by Paul R. Halmos in PDF and/or ePUB format, as well as other popular books in Mathematics & Algebra. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Contents
  5. Preface
  6. 1 Boolean rings
  7. 2 Boolean algebras
  8. 3 Fields of sets
  9. 4 Regular open sets
  10. 5 Elementary relations
  11. 6 Order
  12. 7 Infinite operations
  13. 8 Subalgebras
  14. 9 Homomorphisms
  15. 10 Free algebras
  16. 11 Ideals and filters
  17. 12 The homomorphism theorem
  18. 13 Boolean σ-algebras
  19. 14 The countable chain condition
  20. 15 Measure algebras
  21. 16 Atoms
  22. 17 Boolean spaces
  23. 18 The representation theorem
  24. 19 Duality for ideals
  25. 20 Duality for homomorphisms
  26. 21 Completion
  27. 22 Boolean σ-spaces
  28. 23 The representation of σ-algebras
  29. 24 Boolean measure spaces
  30. 25 Incomplete algebras
  31. 26 Products of algebras
  32. 27 Sums of algebras
  33. 28 Isomorphisms of factors
  34. 29 Isomorphisms of countable factors
  35. 30 Retracts
  36. 31 Projective algebras
  37. 32 Injective algebras
  38. Epilogue
  39. Index