Is there always a diffeomorphism between $(0,1)^2$ and any given (not degenerate) triangle?
Diffeomorphism between a triangle and a square?
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real-analysis
differential-topology
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0Question changed, somebody go for the answer. – 2012-11-28
1 Answers
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If by "triangle" you mean the open set bounded by three line segments (the boundaries themselves are not included), then yes, every convex open subset of the Euclidean plane is diffeomorphic to $\mathbb{R}^2$.
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1I had the Riemannian mapping theorem in mind. – 2012-11-28