Let U⊂Rn (open set) , V⊂Rn and f:U⟶V 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.
Let U⊂Rn (open set) , V⊂Rn and f:U⟶V 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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