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# Lectures on Boolean Algebras Steven Givant

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## Summary

Ann Arbor, Michigan ] anuary, 1963 Contents Section Page 1 1 Boolean rings ............................ 4 Regular open sets . 10 Free algebras . 13 Boolean a-algebras . 15 Measure algebras . 69 17 Boolean spaces . 22 Boolean a-spaces . 24 Boolean measure spaces . 25 Incomplete algebras . 26 Products of algebras . 27 Sums of algebras .

## Lectures on Boolean Algebras Summary

### Lectures on Boolean Algebras by Steven Givant

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 . . .

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 ?-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 ?-spaces.- 23 The representation of ?-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.

NLS9780387900940
9780387900940
0387900942
Lectures on Boolean Algebras by Steven Givant
New
Paperback
Springer-Verlag New York Inc.
1974-01-01
148
N/A
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