Summary.
The main result is that the Jacobian determinant of an analytic open map \( f \colon {\Bbb R}^n \to {\Bbb R}^n \) does not change sign. A corollary of the proof is that the set of branch points of f has dimension \( \le n-2 \).
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Received: February 10, 2000, revised version: October 17, 2000.
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Hirsch, M. Jacobians and branch points of real analytic open maps. Aequat. Math. 63, 76–80 (2002). https://doi.org/10.1007/s00010-002-8006-8
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DOI: https://doi.org/10.1007/s00010-002-8006-8