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March 18th, 2017, 06:51 AM  #11 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,301 Thanks: 94 
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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