Lectures on Boolean Algebras 0387900942, 978-0-387-90094-0, 978-1-4612-9855-7, 1461298555

IN 1959 I lectured on Boolean algebras at the University of Chicago. A mimeographed version of the notes on which the le

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English Pages 148 [153] Year 1974

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Lectures on Boolean Algebras
0387900942, 978-0-387-90094-0, 978-1-4612-9855-7, 1461298555

Author / Uploaded
Paul R. Halmos

Table of contents :
Front Matter....Pages i-vii
Boolean Rings....Pages 1-3
Boolean algebras....Pages 3-9
Fields of sets....Pages 9-12
Regular open sets....Pages 12-17
Elementary relations....Pages 17-21
Order....Pages 21-25
Infinite operations....Pages 25-31
Subalgebras....Pages 31-35
Homomorphisms....Pages 35-40
Free algebras....Pages 40-47
Ideals and filters....Pages 47-51
The homomorphism theorem....Pages 52-55
Boolean σ-algebras....Pages 55-60
The countable chain condition....Pages 61-64
Measure algebras....Pages 64-69
Atoms....Pages 69-72
Boolean spaces....Pages 72-76
The representation theorem....Pages 77-80
Duality for ideals....Pages 81-84
Duality for homomorphisms....Pages 84-90
Completion....Pages 90-97
Boolean σ-spaces....Pages 97-99
The representation of σ-algebras....Pages 100-104
Boolean measure spaces....Pages 104-108
Incomplete algebras....Pages 109-115
Products of algebras....Pages 115-118
Sums of algebras....Pages 119-122
Isomorphisms of factors....Pages 122-126
Isomorphisms of countable factors....Pages 126-130
Retracts....Pages 130-136
Projective algebras....Pages 137-140
Injective algebras....Pages 140-143
Epilogue....Pages 144-144
Back Matter....Pages 145-147