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1、RealAlgebraicManifoldsJohnNashTheAnnalsofMathematics,2ndSer.,Vol.56,No.3.(Nov.,1952),pp.405-421.StableURL:http://links.jstor.org/sici?sici=0003-486X%28195211%292%3A56%3A3%3C405%3ARAM%3E2.0.CO%3B2-BTheAnnalsofMathematicsiscurrentlypublishedbyAnnalsofMathematics.YouruseoftheJSTORarchiveind
2、icatesyouracceptanceofJSTOR'sTermsandConditionsofUse,availableathttp://www.jstor.org/about/terms.html.JSTOR'sTermsandConditionsofUseprovides,inpart,thatunlessyouhaveobtainedpriorpermission,youmaynotdownloadanentireissueofajournalormultiplecopiesofarticles,andyoumayusecontentintheJSTORarc
3、hiveonlyforyourpersonal,non-commercialuse.Pleasecontactthepublisherregardinganyfurtheruseofthiswork.Publishercontactinformationmaybeobtainedathttp://www.jstor.org/journals/annals.html.EachcopyofanypartofaJSTORtransmissionmustcontainthesamecopyrightnoticethatappearsonthescreenorprintedpag
4、eofsuchtransmission.TheJSTORArchiveisatrusteddigitalrepositoryprovidingforlong-termpreservationandaccesstoleadingacademicjournalsandscholarlyliteraturefromaroundtheworld.TheArchiveissupportedbylibraries,scholarlysocieties,publishers,andfoundations.ItisaninitiativeofJSTOR,anot-for-profito
5、rganizationwithamissiontohelpthescholarlycommunitytakeadvantageofadvancesintechnology.FormoreinformationregardingJSTOR,pleasecontactsupport@jstor.org.http://www.jstor.orgFriOct2618:13:362007ANNALSOFMATHEMATICSVol.56,No.3,November,1952PrintedinU.S.A.REALALGEBRAICMANIFOLDSBYJOIINSASH(Recei
6、vedOctober8,1951)IntroductionThemainpurposeofthispaperistodevelopsomeconnectionsbetweendif-ferentialgeometryandrealalgebraicgeometry.Theseconnectionsconcernthegeometricalformsthatcanbeassumedbyarealalgebraicvariety.Ourfirsttheoremassertsthatanycloseddifferentiablemanifoldcanbedis-playeda
7、sanon-singularportionofarealalgebraicvariety.Morespecifically,anydifferentiableimbeddingofthemanifoldmaybeapproximatedbysuchanalgebraicimbeddingofit.Theexistenceofthesealgebraicmodelsofdifferentiablemanifoldssuggestedtheformulationofanabstractconceptofadifferentiablemanif
