Let A C Rn be an open set and f : A Rn a continuously differentiable 1-1

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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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An Introduction to Analysis

ISBN: 978-0132296380

4th edition

Authors: William R. Wade

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Question Posted: Oct 01, 2009 01:28 AM

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Let A C Rn be an open set and f : A Rn a continuously differentiable 1-1

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An Introduction to Analysis

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