Let be a continuous function which is 1-1 on any open set in . Prove that is 1-1 throughout the domain.
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Originally Posted by Chandru1 Let be a continuous function which is 1-1 on any open set in . Prove that is 1-1 throughout the domain. Solution 1 (The wiseguy solution): is open in itself and thus, according to the given data, is 1-1 there. Solution 2: is open so is 1-1 there. Now, if , for some ,then take ... By the way , the continuity of isn't required. Tonio
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