Lectures on Boolean Algebras

  • Paul R. Halmos

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Paul R. Halmos
    Pages 1-3
  3. Paul R. Halmos
    Pages 3-9
  4. Paul R. Halmos
    Pages 9-12
  5. Paul R. Halmos
    Pages 12-17
  6. Paul R. Halmos
    Pages 17-21
  7. Paul R. Halmos
    Pages 21-25
  8. Paul R. Halmos
    Pages 25-31
  9. Paul R. Halmos
    Pages 31-35
  10. Paul R. Halmos
    Pages 35-40
  11. Paul R. Halmos
    Pages 40-47
  12. Paul R. Halmos
    Pages 47-51
  13. Paul R. Halmos
    Pages 52-55
  14. Paul R. Halmos
    Pages 55-60
  15. Paul R. Halmos
    Pages 61-64
  16. Paul R. Halmos
    Pages 64-69
  17. Paul R. Halmos
    Pages 69-72
  18. Paul R. Halmos
    Pages 72-76
  19. Paul R. Halmos
    Pages 77-80
  20. Paul R. Halmos
    Pages 81-84

About this book

Introduction

IN 1959 I lectured on Boolean algebras at the University of Chicago. A mimeographed version of the notes on which the lectures were based circulated for about two years; this volume contains those notes, corrected and revised. Most of the corrections were suggested by Peter Crawley. To judge by his detailed and precise suggestions, he must have read every word, checked every reference, and weighed every argument, and I am lIery grateful to hirn for his help. This is not to say that he is to be held responsible for the imperfec­ tions that remain, and, in particular, I alone am responsible for all expressions of personal opinion and irreverent view­ point. P. R. H. Ann Arbor, Michigan ] anuary, 1963 Contents Section Page 1 1 Boolean rings ............................ . 2 Boolean algebras ......................... . 3 9 3 Fields of sets ............................ . 4 Regular open sets . . . . . . . . . . . . . . . . . . . 12 . . . . . . 5 Elementary relations. . . . . . . . . . . . . . . . . . 17 . . . . . 6 Order. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 . . . . . . . . . 7 Infinite operations. . .. . . . . . . . . . . . . . . . . 25 . . . . . 8 Subalgebras . . . . . . . . . . . . . . . . . . . . .. . . . 31 . . . . . . 9 Homomorphisms . . . . . . . . . . . . . . . . . . . . 35 . . . . . . . 10 Free algebras . . . . . . . . . . . . . . . . . . . . . . 40 . . . . . . . 11 Ideals and filters. . . . . . . . . . . . . . . . . . . . 47 . . . . . . 12 The homomorphism theorem. . . . . . . . . . . . .. . . 52 . . 13 Boolean a-algebras . . . . . . . . . . . . . . . . . . 55 . . . . . . 14 The countable chain condition . . . . . . . . . . . . 61 . . . 15 Measure algebras . . . . . . . . . . . . . . . . . . . 64 . . . . . . . 16 Atoms.. . . . .. . . . . .. .. . . . ... . . . . .. . . ... . . .. 69 17 Boolean spaces . . . . . . . . . . . . . . . . . . . . 72 . . . . . . . 18 The representation theorem. . . . . . . . . . . . . . 77 . . . 19 Duali ty for ideals . . . . . . . . . . . . . . . . . .. . . 81 . . . . . 20 Duality for homomorphisms . . . . . . . . . . . . . . 84 . . . . 21 Completion . . . . . . . . . . . . . . . . . . . . . . . 90 . . . . . . . . 22 Boolean a-spaces . . . . . . . . . . . . . . . . . .. . . 97 . . . . . 23 The representation of a-algebras . . . . . . . . .. . . 100 . 24 Boolean measure spaces . . . . . . . . . . . . . .. . . 104 . . . 25 Incomplete algebras . . . . . . . . . . . . . . . .. . . 109 . . . . . 26 Products of algebras . . . . . . . . . . . . . . . .. . . 115 . . . . 27 Sums of algebras . . . . . . . . . . . . . . . . . .. . . 119 . . . . . 28 Isomorphisms of factors . . . . . . . . . . . . . .. . . 122 . . .

Keywords

Boolean algebra Boolesche Algebra Factor Finite Morphism Volume algebra boundary element method duality homomorphism measure presentation sets theorem university

Authors and affiliations

  • Paul R. Halmos
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-9855-7
  • Copyright Information Springer-Verlag New York 1974
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90094-0
  • Online ISBN 978-1-4612-9855-7
  • Series Print ISSN 0172-6056
  • About this book