文档介绍：ElementaryRealand
Cornplex Analysis
TRANSLATEDAND EDITEDBY
REVISEDENGLISH EDITION
DOVER PUBLICATIONS,INC.
NewYork
Copyright
Copyright1973 theby Massachusetts Institute ofTe chnology .
©
Allrights reserved under Pan American and International Copyright
Conventions.
BibliographicalNote
ThisDover edition, firstpublished in1996, isan unabridged, corrected
republicationofthe work first published inEnglish byThe MIT Press,
Cambridge,Massac husetts,1973, as Volume 1 ofthe two-volume course
"MathematicalAnalysis."
LibraryofCongress Cataloging-in-Publication Data
Shilov,G. E. (iI Evgen'evich)
[MatematicheskiIanaliz. Chasti 1-2. English]
plex analysis i E. Shilov ;revised
/
Englishedition translated andedited byRichard Silverman. A.
p. em.
Originallypublished inEnglish: Cambridge, Mass. :MIT Press,1973.
Includes index.
ISBN0-486-68922-0 (pbk.)
analysis. Silverman, I. Richard A. .
515-dc20 95-37030
CIP
Manufacturedinthe United StatesofAmerica
DoverPublications, Inc.,31East 2nd Street, Mineola,
Contents
Preface
IX
1 RealNUDlbers
I.!.Set-Theoretic Preliminaries I
forthe Real Number System 3
ofthe Addition Axioms 4
ofthe Mult iplication Axioms 5
ofthe Order Axioms 9
ofthe Least Bound AxiomUpper 12
Principle ofArchimedes andIts Consequences 16
Principle ofNested Intervals 21
Exte ndedReal Number System 22
Problems 24
2 Sets
onSe ts 27
ofSets 29
Sets 31
Sets 33
Structures 35
-Dimensional Space 39
Numbers 43
andGraphs 48
Problems 50
3Metric Spaces
andExamples 53
Sets 61
Sequencesand Homeomorphisms 63
Points