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seen May 20 at 23:41

Oct
27
awarded  Popular Question
Jul
2
awarded  Curious
Jan
11
awarded  Nice Question
Jun
7
accepted An example of a space which fails to be compactly generated
Jun
7
revised An example of a space which fails to be compactly generated
edited body
Jun
5
revised An example of a space which fails to be compactly generated
deleted 6 characters in body
Jun
4
asked An example of a space which fails to be compactly generated
Apr
22
awarded  Disciplined
Apr
19
accepted The structure $(\mathbb{Q}, <)$ is O-minimal
Apr
17
accepted a special case of the fundamental normality theorem for Riemann surfaces
Apr
17
comment a special case of the fundamental normality theorem for Riemann surfaces
no problem. I think I understand your edit. Your solution is very elegant! Thanks for the help.
Apr
16
comment a special case of the fundamental normality theorem for Riemann surfaces
In my previous comment I was really thinking of $K$ as being inside some chart and homeomorphic to some closed ball. I completely agree with you on saying we have to pass to the covers, but where I get confused is when we have to push back down to $\mathbb{C}\setminus\{0,1\}$ through $q$. However, it is not immediate to me that $q$ will preserve uniformly convergent sequences of functions. I apologize for hassling you, I appreciate the time you have taken to help me!
Apr
16
comment a special case of the fundamental normality theorem for Riemann surfaces
Thanks for the answer! I was actually having trouble with the first part. I had thought of trying to prove it by looking at compact subsets $K$ with nonempty interior in evenly covered neighborhoods, and then using the fact that $\widetilde{f}_{n_k}\to \widetilde{f}$ uniformly on any component of the preimage $p^{-1}(K)$. However, its not clear to me how to prove $\|q\widetilde{f}_{n_k}-q\widetilde{f}\|\to 0$ on this compact subset. Perhaps I am missing something though.
Apr
16
asked a special case of the fundamental normality theorem for Riemann surfaces
Apr
16
awarded  Informed
Mar
11
comment Proving some properties of pointwise convergent sequences.
Well you use this identity (which can be checked directly) and then use the triangle inequality. Remember, to show that $f_n\to f$ pointwise one must show that $|f_n(x)-f(x)|\to 0$ for all $x$. So using the fact that $f_n\to f$ and $g_n\to g$ pointwise, and using this identity will show that $|f_ng_n(x)-fg(x)|\to 0$ for all $x$
Mar
11
comment Proving some properties of pointwise convergent sequences.
For the first one note that $f_ng_n-fg = (f_n-f)(g_n-g)+f(g_n-g)+g(f_n-f)$
Feb
14
awarded  Yearling
Feb
14
answered Entire function with prescribed values
Dec
20
answered Model Theory and Topology Connections