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Results tagged with infinite-dimensional-manifolds
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user 153173
2
votes
0
answers
106
views
Open embedding of non-separable infinite dimensional manifolds
It is well-known (see here) that separable infinite-dimensional topological Hilbert manifolds can be embedded as open sets of the modeling separable Hilbert space. Using that separable Fréchet (in par …
6
votes
1
answer
508
views
CW structure on infinite-dimensional manifolds
It is well-known (due to this work of Palais, I believe) that Banach manifolds are dominated by countable CW complexes. It then follows (due Whitehead, as indicated by Milnor in this work) that they h …
4
votes
0
answers
190
views
Generalizations of Sard-Smale Theorem
Sard-Smale theorem holds for Fredholm maps $f:M\rightarrow B$ between separable Banach manifolds $M,N$. There are some constrains relating the Fredholm index $\operatorname{ind}(f)$ of $f$ to its diff …