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Jun 30, 2013 at 9:33 comment added Ritwik I am not seeing why $\pi(X_i)$ is contained inside a FINITE union of manifolds of dimension less than or equal to the dimension of $X_i$. The image of $X_i$ need not be smooth.
Jun 30, 2013 at 9:27 history answered Peter Michor CC BY-SA 3.0