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Aug 23, 2013 at 0:30 comment added David Roberts The problem is that a map of Fréchet manifolds admitting (enough) local sections is not enough to make it a submersion: it is a strictly stronger notion. And the reason one wants submersions is to ensure certain pullbacks exist, as in the finite-dimensional case.
Feb 8, 2013 at 14:56 history answered Christoph Wockel CC BY-SA 3.0