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 Feb16 awarded Yearling Oct27 awarded Popular Question Jul2 awarded Curious Jan11 awarded Nice Question Jun7 accepted An example of a space which fails to be compactly generated Jun7 revised An example of a space which fails to be compactly generated edited body Jun5 revised An example of a space which fails to be compactly generated deleted 6 characters in body Jun4 asked An example of a space which fails to be compactly generated Apr22 awarded Disciplined Apr19 accepted The structure $(\mathbb{Q}, <)$ is O-minimal Apr17 accepted a special case of the fundamental normality theorem for Riemann surfaces Apr17 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. Apr16 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! Apr16 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. Apr16 asked a special case of the fundamental normality theorem for Riemann surfaces Apr16 awarded Informed Mar11 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 $x$ Mar11 comment Proving some properties of pointwise convergent sequences. For the first one note that $f_ng_n-fg = (f_n-f)(g_n-g)+f(g_n-g)+g(f_n-f)$ Feb14 awarded Yearling Feb14 answered Entire function with prescribed values