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A smooth map on a Banach manifold whose pointwise rank is finite but its rank is not globally bounded
Is there a connected Banach manifold $M$ and a smooth map $f:M \to M$ such that the rank of $Df_x$ is finite for every $x\in M$ but this rank is not uniformly bounded
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3
votes
1
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Is $C^\nu(X,Y)$ a Banach manifold and a Lindelöf space?
Suppose that $X$ is a compact, finite dimensional manifold and $Y$ is an infinite dimensional, second countable ($C^\infty$-)Banach manifold. Let $\nu \in \mathbb{N}$.
Question: Is the space $C^\nu(...
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