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Is it possible to extend a diffeomorphism of $[0,1]^n$ to a diffeomorphism of a compact infinite-dimensional manifold?

For example, we can always extend a diffeomorphism $f$ of $[0,1]^n$ to a diffeomorphism $g$ of $[0,1]^m$ for $m >n$ by $g(x_1,...,x_n,...,x_m)=(f(x_1,...,x_n),x_{n+1},...,x_m)$.

Is there an analogous method from $[0,1]^n$ to a compact infinite-dimensional manifold?

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yes, more something like this. –  user8991 Oct 25 '13 at 0:23
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