2000 Mathematics Subject Classification. Primar y 26-XX .
Fron t cover : Th e cove r illustrate s ho w continuou s function s ca n converg e nonuni -
formly t o a discontinuou s function . I t i s base d o n Figur e 17.1 , pag e 76 . Th e ball s i n
the backgroun d illustrat e a n ope n cover , a s i n th e definitio n o f th e importan t concep t o f
compactness (Chapte r 9 , pag e 41).
Bac k cover : Th e author , i n th e Mat h Librar y outsid e hi s offic e a t William s College .
Photo b y Cesa r Silva .
Cover desig n b y Eri n Murph y o f th e America n Mathematica l Society , o n a suggestio n
by E d Burger .
For additiona l informatio n an d update s o n thi s book , visi t
w w w . a m s . o r g / b o o k p a g e s / r e a l
Library o f Congres s Cataloging-in-Publicatio n D a t a
Morgan, Frank .
Real analysi s / Fran k Morgan .
p. cm.
Includes index .
ISBN 0-8218-3670-6 (alk . paper)
1. Mathematica l analysis . I . Title .
QA300.M714 200 5
515—dc22 200504122
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Reprinted wit h correction s b y the American Mathematica l Society , 2012.
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