OPEN DIFFERENTIABLE MAPPINGS
Keywords:
open mapping, topological dimension, differentiable functionAbstract
It is a well-known result that a $\mathcal C^1$-mapping defined on an open subset $ \Omega$ of a Banach space $E$ with values in a Banach space $F$ whose differential is everywhere onto is an open mapping from $\Omega$ onto an open subset of $F$. We prove that this result still holds if $E$ is finite-dimensional and both the critical set and the set of critical values have small topological dimensions. The restriction on the set of critical values can be removed if $E$ and $F$ have same dimension.Downloads
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