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克莱因瓶是一个不可定向的二维紧流形，而球面或轮胎面是可克莱因瓶克莱因瓶定向的二维紧流形。如果观察克莱因瓶，有一点似乎令人困惑－－“67P/楚留莫夫-格拉希门克”彗星[67]在太CHAPTERX.TOBACCOOFFERINGS..ItwasabeautifulmoonlighteveninginAugust.Ashadowyhazelingeredovertheriver,whichglistenedandsparkledinthemoonlight.TheChiefandseveralmembersofhisfamilywereseatedonthebeachinfrontoftheWigwamlisteningtotheHonorableJosephPapineau,who,withhisson,LouisJoseph,had