How to think about diffeomorphisms
No.13951983 ViewReplyOriginalReport
Quoted By: >>13951985 >>13952007
The idea of a homeomorphism is intuitively clear to me as a bijective continous deformation.
A diffeomorphism is also a homeomorphism
(M and N being smooth manifolds)
only with the added caviat that be differentiable for all charts on M and N.
What I think when I hear the term diffeomorphism is intuitively a continous bijective deformation that doesn't create or delete any edges or corners (along with their higher dimensional analouges) (ie it has a unique n-dimensional tangent space at every point).
Is this the correct interpretation? And if so how does it follow from the definition?
A diffeomorphism is also a homeomorphism
(M and N being smooth manifolds)
only with the added caviat that be differentiable for all charts on M and N.
What I think when I hear the term diffeomorphism is intuitively a continous bijective deformation that doesn't create or delete any edges or corners (along with their higher dimensional analouges) (ie it has a unique n-dimensional tangent space at every point).
Is this the correct interpretation? And if so how does it follow from the definition?
