Carl Wienecke
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 Aug 27 comment When are the limit operations commutative? It might help if you could be more specific about what sorts of limits you're talking about. Aug 25 answered Continuity of function $\lim_{t \rightarrow x} f(t)$ Aug 25 answered Why is the last step of proof by induction necessary? Aug 24 awarded Teacher Aug 24 answered topology - analysis Book Aug 21 comment A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$ Thanks LVK I'll have a look at that answer. The mathforum thread does not provide a full proof but (I believe) I was able to trivially verify smoothness, bijectivity, and nonsingularity of the function $x \mapsto x \int_0^1 \frac{dt}{f(xt)}$ Aug 20 comment A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$ Thanks t.b. A little more googling turned up this mathforum.org/kb/… which to my amazement seems to be an extremely elementary proof of the statement. I feel like I must be missing something. Aug 20 comment A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$ Thanks again. It will take me a bit to digest this. Aug 20 comment A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$ Thanks, LVK. Yeah that was something that led me to believe that the proof was long and complicated which makes me puzzled by the fact that it was assigned as a homework problem (albeit for extra credit and at Columbia) Aug 20 awarded Editor Aug 20 awarded Student Aug 20 revised A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$ edited title Aug 20 asked A star shaped open set in $\mathbb{R}^n$ is diffeomorphic to $\mathbb{R}^n$