Carl Wienecke

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visits member for 1 year, 10 months
seen Sep 5 '12 at 8:10

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 the last step of proof by induction is 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 $\mathbb{R}^n$