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 March 18th, 2017, 06:51 AM #11 Senior Member   Joined: Mar 2015 From: New Jersey Posts: 969 Thanks: 78 Assume f is homeomorphic from M1 to M2 in E Let M! be open and bounded. Let M2 be closed and bounded. (compact) M1=f$\displaystyle ^{-1}$(M2) is compact. Contradiction.

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### can an open set be homeomorphic to a closed set ?

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