Is there a similar statement to the constant rank theorem for finite dim real smooth manifolds which holds for a smooth map $F:B \rightarrow M$ where $B$ is an infinite (countable) dim Banach space and $M$ is a finite dim real smooth manifold?
constant rank theorem for banach spaces
reference-requestdg.differential-geometryfa.functional-analysislinear-algebraoc.optimization-and-control
Benjamin
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