[幾何] local diffeomorphism
我想請問 local diffeomorphism 有沒有下述的性質
Let M,N be differentiable manifolds, and f:M --> N be a local diffeomorphism.
Suppose Z is a closed subset in N such that the restriction
f|_{f^{-1}(Z)}: f^{-1}Z --> Z
is a bijection.
Then there exists an open neighborhood U of f^{-1}Z such that the restriction
f|_U: U --> f(U) is a diffeomorphism.
(Prove or disprove)
謝謝
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