Transcription of paper.' - pnas.org
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paper.' - pnas.org
, "'Itisprovedbyconstructingan"abstract"ma ppingcylinderofXandtran-scribingintoalge braictermstheproofoftheanalogoustheoremo nCW-complexes.*Thisnotearosefromconsulta tionsduringthetenureofaJohnSimonGuggenhe imMemorialFellowshipbyMacLane.'Whitehead , ,"CombinatorialHomotopyIandII," ,55,214-245and453-496(1949).Werefertothe sepapersasCHIandCHII,respectively.'Byaco mplexweshallmeanaconnectedCWcomplex,asde finedin ,S.,"CohomologyTheoryinAbstractGroupsIII ," ,50,736-761(1949),referredtoasCTIII.'An( unpublished) ( )thestrongerhypothesisthatXBcontainsthec enterofA,butalltherelevantdevelopmentsth ereapplyundertheweakerassumption( ).
MATHEMATICS: J. F. NASH,JR. This follows from the arguments used in a forthcoming paper."' It is proved by constructing an "abstract" mapping cylinder of X and tran ...
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