Springer.Lee.J.M.Introduction.to.topological.manifolds.(Springer.GTM202.2000)(errata)(5s)

《Springer.Lee.J.M.Introduction.to.topological.manifolds.(Springer.GTM202.2000)(errata)(5s)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、CorrectionstoIntroductiontoTopologicalManifoldsbyJohnM.LeeJanuary24,2005Changesoradditionsmadeinthepastsixmonthsaredated.•Page29,statementofLemma2.11:Thesecondsentenceshouldbereplacedby“IftheopensubsetsofXareexactlythosesetsthatsatisfythebasiscriterionwithrespecttoB,thenBisabasisforthetopo

2、logyofX.”•Page29,paragraphbeforeExercise2.15:Insteadof“thetopologiesofExercise2.1,”itshouldsay“someofthetopologiesofExercise2.1.”•Page30,lastsentenceoftheproofofLemma2.12:ReplaceUbyf−1(U)(threetimes).•Page30,firstparagraphinthe“Manifolds”section:Deletethesentence“LetXbeatopologicalspace.”•P

3、age38,Problem2-16(b):Replacepart(b)by“ShowthatforanyspaceY,amapf:X→Yiscontinuousifandonlyifpn→pinXimpliesf(pn)→f(p)inY.”•Page38,Problem2-18:ThisproblemshouldbemovedtoChapter3,becauseIntMand∂Maretobeinterpretedashavingthesubspacetopologies.Also,forthisproblem,youmayusewithoutproofthefacttha

4、tIntMand∂Maredisjoint.•Page40,lastlineofExample3.1:Replace“subspacetopologyonB”by“subspacetopologyonC.”•Page47,line5frombottom:Replace“nextlemma”by“nexttheorem.”•Page51,proofofProposition3.13,thirdline:f1(U1),...,fk(Uk)shouldbereplacedby−1−1f1(U1),...,fk(Uk).•Page51,proofofProposition3.14,

5、lastsentence:Replace“theprecedinglemma”by“theprecedingproposition.”•Page52,firstparagraphafterExercise3.8:Inthefirstsentence,replacethewords“surjectiveandcontinuous”by“surjective.”Also,addthefollowingsentenceattheendoftheparagraph:“Itisimmediatefromthedefinitionthateveryquotientmapiscontinuou

6、s.”•Page52,lastparagraph:Changetheword“quotient”to“surjective”inthefirstsentenceoftheparagraph.•Page53,line1:Changetheword“quotient”to“surjective”atthetopofthepage.•Page53,Lemma3.17:Addthefollowingsentenceattheendofthestatementofthelemma:(Moreprecisely,ifU⊂Xisasaturatedopenorclosedset,thenπ

7、

8、U:U→π(U)isaquotientmap.)(1/24/05)Page81,firstdisplayedequation:ThedefinitionofFshouldbe−1x

9、x

10、f,x6=0;F(x)=

11、x

12、0,x=0.1(1/24/05)Page81,firstlineafterthedisplayedequation:Replacethefirstsentencebythefollowing:“ThenFiscontinuousawayfromtheoriginbecausef−1is,andatt