Givant etal - Introduction to Boolean Algebras.pdf

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Undergraduate Texts in Mathematics
Editors:
S. Axler
K.A. Ribet
Undergraduate Texts in Mathematics
For other titles published in this series, go to
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Steven Givant
Paul Halmos
Introduction to Boolean
Algebras
ABC
Steven Givant
Mills College
Department of Mathematics
Paul Halmos
(Deceased)
and Computer Science
5000 MacArthur Blvd
Oakland CA 94613-1301
USA
givant@mills.edu
Editorial Board
S. Axler
Mathematics Department
San Francisco State University
San Francisco, CA 94132
USA
axler@sfsu.edu
K.A. Ribet
Department of Mathematics
University of California
at Berkeley
Berkeley, CA 94720
USA
ribet@math.berkeley.edu
ISSN: 0172-6056
ISBN: 978-0-387-40293-2
e-ISBN: 978-0-387-68436-9
DOI: 10.1007/978-0-387-68436-9
Library of Congress Control Number: 2008939810
Mathematics Subject Classication (2000): 06Exx
Springer Science+Business Media, LLC 2009
All rights reserved. This work may not be translated or copied in whole or in part without the written
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10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection
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The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are
not identied as such, is not to be taken as an expression of opinion as to whether or not they are subject
to proprietary rights.
Printed on acid-free paper
springer.com
c
Contents
Preface
ix
1BooleanRings 1
Exercises ................................ 5
2 Boolean Algebras 8
Exercises ................................ 11
3 Boolean Algebras Versus Rings 14
Exercises ................................ 18
4 The Principle of Duality 20
Exercises ................................ 22
5 Fields of Sets 24
Exercises ................................ 28
6 Elementary Relations 31
Exercises ................................ 33
7Order 38
Exercises ................................ 42
8 Innite Operations 45
Exercises ................................ 49
9 Topology 53
Exercises ................................ 61
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