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2SHANKARAPAILOORconcludesection2.1bydeningthesenotions.Webeginsection 2SHANKARAPAILOORconcludesection2.1bydeningthesenotions.Webeginsection

2SHANKARAPAILOORconcludesection2.1byde ningthesenotions.Webeginsection - PDF document

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2SHANKARAPAILOORconcludesection2.1byde ningthesenotions.Webeginsection - PPT Presentation

4SHANKARAPAILOORCorollary27LetMbecompactandfMNanalyticIffisnotconstantthenfMNAsasmoothmanifoldMcarrieskformswhichwedenoteby kMCsee3or5forde nitionThatbeingsaid 0MCaresimplyC1 ID: 121411

4SHANKARAPAILOORCorollary2.7.LetMbecompactandf:M!Nanalytic.Iffisnotconstant thenf(M)=N.Asasmoothmanifold Mcarriesk-formswhichwedenoteby k(M;C)(see[3]or[5])forde nition.Thatbeingsaid 0(M;C)aresimplyC1

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