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1、ProblemBooksinMathematicsSeriesEditorPeterWinklerDepartmentofMathematicsDartmouthCollegeHanover,NH03755USApeter.winkler@dartmouth.eduForothertitlespublishedintheseries,gotowww.springer.com/series/714.VladimirV.TkachukACp-TheoryProblemBookTopologicalandFunctionSpacesVladimirV.
2、TkachukDepartamentodeMatema´ticasUniversidadAuto´nomaMetropolitanaAv.SanRafaelAtlixco,186,Col.VicentinaIztapalapa09340,MexicoCityMexicovova@xanum.uam.mxISSN0941-3502ISBN978-1-4419-7441-9e-ISBN978-1-4419-7442-6DOI10.1007/978-1-4419-7442-6SpringerNewYorkDordrechtHeidelbergLondo
3、nMathematicsSubjectClassification(2010):54C35LibraryofCongressControlNumber:2011923537#SpringerScienceþBusinessMedia,LLC2011Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringS
4、treet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthisp
5、ublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)PrefaceT
6、hisbookwasconceivedasanintroductiontoCp-theorywiththeintentthatitcouldalsobeusedasareferenceguideforspecialists.Theauthorsideawastomakethisintroductionaccessibletoanyreaderhavingaminimumofmathematicalcultureand,possibly,withnotopologicalbackgroundatall.Thisworkisauniqueattemp
7、ttoofferanyundergraduatestudentanopportunitytoplungedirectlyintothetheoryoffunctionspacesendowedwiththetopologyofpointwiseconvergence.ThemaindifficultyinthisquestistoachievethelevelofunderstandingingeneraltopologyneededtobeabletoworkinCp-theory.Itoftenhappensthatastudentwhowan
8、tstostudyfunctionspacesistoldthathe(orshe)hasfirsttolearnsomegeneralt
