Wednesday, 10 October 2018

real analysis - Let UsubsetmathbbRn (open set) and f:UlongrightarrowV a homeomorphism then we can say that V is a open set in mathbbRn,?



Let URn (open set) , VRn and f:UV a homeomorphism then we can say that V is a open set in Rn ?




Any hints would be appreciated.


Answer



Yes, this result goes by the name Invariance of Domain and is due to Brouwer. It's a non-trivial result.


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