[數撚圍爐區] 越上連登越唔識數學架 (15)
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點解partition of unity 對於manifold咁重要
睇唔明Ck manifold同C-inf manifold
有一個Whitney既result係 for k> 1, for any Ck manifold, the maximal atlas contains a C-inf atlas, ie, smooth structures in Ck manifold
睇wiki直頭話one uses differentiable manifold, smooth manifold interchangeably
但in R1-3, up to diffeomorphism, there is a unique smooth structure one can make of a given topology.而又有所謂exotic R4
唔係好明即係點?係咪所有Ck manifold 都可以睇成C-inf manifold?咁既話exotic R4又咩黎
有一個Whitney既result係 for k> 1, for any Ck manifold, the maximal atlas contains a C-inf atlas, ie, smooth structures in Ck manifold
睇wiki直頭話one uses differentiable manifold, smooth manifold interchangeably
但in R1-3, up to diffeomorphism, there is a unique smooth structure one can make of a given topology.而又有所謂exotic R4
唔係好明即係點?係咪所有Ck manifold 都可以睇成C-inf manifold?咁既話exotic R4又咩黎
即係話分別係用邊款differentiable structure去睇個topological manifold?
