Let F be a continuous map of a closed ball in ${\mathbb R}^m$ to ${\mathbb R}^n$ where $m\ge n$. Suppose that F is open i.e. images of all open sets are open. Is it true that for any point of the interior of the image of F, the image of any sufficiently $C^0$ close maps covers this point?
I believe, this must be something about Topologic Index Theory.
Thank you very much! Is it written somewhere? Could you please give me a reference? Just the name of a book...
Probably, I can prove the statement myself but this would be not too good for article...
Thanks a lot in advance!
Topological index and openness can be seen in
Yu.Yu. Trokhimchuk Continuous mappings of domains in euclidean space// Ukr. Mat. Zh. 16, 196-211 (1964).
And in my book
https://www.researchgate.net/publication/268605683_Topological-algebraic_structures_and_geometric_methods_in_complex_analysis
Book Topological-algebraic structures and geometric methods in co...
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