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Statement of a problem № m612

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Let A C Rn be an open set and f : A-> Rn a continuously differentiable 1-1 function such that det f1 (x) ≠ 0 for all . Show that f (A) is an open set and f -1: f (A) ->A is differentiable. Show also that f (b) is open for any open set B C A.




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