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- Mar 10, 2012

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I am not sure what the definition of a diffeomorphism is.

In Spivak's 'Calculus on Manifolds', it is defined as:

A

**diffeomorphism**is a function $h:U\to V$, $U$ and $V$ are open sets in $\mathbb R^n$, such that $h$ is differentiable and has a differentiable inverse.

I have seen the following in Lee's 'Introduction to Smooth Manifolds':

Let $U$ and $V$ be open subsets in $\mathbb R^n$.

A function $F:U\to V$ is

**smooth**if each component of $F$ has continuous partial derivatives of all orders.

A function $h:U\to V$ is a

**diffeomorphism**if it is smooth and has a smooth inverse.

The one in Lee's book is far stronger than the one in Spivak.

I am not sure which one is 'more' standard.

Does this puzzle you too?