Submission date: 3 June 2021

Abstract:

In this paper, we give a characterization of openness of definable non-smooth mappings. More precisely, for a definable continuous mapping f from a definable connected open subset Ω of ℝ^n into ℝ^n, we will show that the following two statements are equivalent:
(i) The mapping f is open.
(ii) The fibers of f are finite and the Jacobian of f does not change sign on the set of points at which f is differentiable.

Mathematics Subject Classification:

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Full text arXiv 2106.01593: pdf, ps.