资源描述：
《Springer.Bridges.D.Foundations.Of.Real.And.Abstract.Analysis.(Gtm.174.Springer.1998)(323s)》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、Dedicatedtothememoryofmyparents:DouglasMcDonaldBridgesandAllisonHoggSweetAnalytics,’tisthouhastravishedme.Faustus(Marlowe)Thestonewhichthebuildersrefusedisbecometheheadstoneofthecorner.Psalmcxviii,22....fromsosimpleabeginningendlessformsmostbeautifulandmostwonderfulhavebeen,andarebeing,evo
2、lved.Theoriginofspecies(Darwin)PrefaceThecoreofthisbook,Chapters3through5,presentsacourseonmetric,normed,andHilbertspacesatthesenior/graduatelevel.ThemotivationforeachofthesechaptersisthegeneralisationofaparticularattributeofthenEuclideanspaceR:inChapter3,thatattributeisdistance;inChapter4
3、,length;andinChapter5,innerproduct.Inadditiontothestandardtopicsthat,arguably,shouldformpartofthearmouryofanygraduatestudentinmathematics,physics,mathematicaleconomics,theoreticalstatistics,...,thispartofthebookcontainsmanyresultsandexercisesthatareseldomfoundintextsonanalysisatthislevel.E
4、xamplesofthelatterareWong’sTheorem(3.3.12)showingthattheLebesguecoveringpropertyisequivalenttotheuniformcontinuityproperty,andMotzkin’sresult(5.2.2)thatanonemptyclosedsubsetofEuclideanspacehastheuniqueclosestpointpropertyifandonlyifitisconvex.Thesadrealitytodayisthat,perceivingthemasoneoft
5、heharderpartsoftheirmathematicalstudies,studentscontrivetoavoidanalysiscoursesatalmostanycost,inparticularthatoftheirowneducationalandtechnicaldeprivation.Manyuniversitieshaveattimescapitulatedtothenegativedemandofstudentsforanalysiscoursesandhaveseriouslywatereddowntheirexpectationsofstud
6、entsinthatarea.Asaresult,mathematicsma-jorsaregraduating,sometimeswithhighhonours,withlittleexposuretoanythingbutarudimentarycourseortwoonrealandcomplexanalysis,oftenwithoutevenanintroductiontotheLebesgueintegral.Forthatreason,andalsoinordertoprovideareferenceformaterialthatisusedinlaterch
7、apters,Ichosetobeginthisbookwithalongchapterprovidingafast–pacedcourseofrealanalysis,coveringconver-xPrefacegenceofsequencesandseries,continuity,differentiability,and(RiemannandRiemann–Stieltjes)integration.Theinclusionofthatchaptermeansthattheprerequisiteforth
