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 May27 accepted Characterization of proper maps using filters May25 comment Characterization of proper maps using filters @HennoBrandsma: It is not clear to me how I would use this to prove that $f$ is closed in the proof of the reverse implication: Pick a $y$ and an open $O$ such that $A := f^{-1}(\{y\}) \subseteq O$. Let $\mathcal U$ be an ultrafilter finer than $A$. Supposing $A$ is compact, $\mathcal U$ converges to some $x \in A$, hence $f[\mathcal U]$ converges to $y$. Since $\mathcal U$ contains $O$, we have that $f(O) \in f[\mathcal U]$, which means that $f(O)$ intersects every open set containing $y$. From this, how do I find a open $V$ such that $f^{-1}(V) \subseteq O$? May25 comment Characterization of proper maps using filters Of course! Thanks. May25 comment Characterization of proper maps using filters I don't see the contradiction. $f(U) \subseteq W$ implies that $U \subseteq f^{-1}(W)$ and I know that $f^{-1}(W)$ is open and contains $A$. May24 revised Characterization of proper maps using filters added 779 characters in body May24 comment Characterization of proper maps using filters Nevermind. I see that $\mathcal U_C$ is the trace of $\mathcal U$ on $C$. But it is not clear that the trace would exist to begin with. May24 comment Characterization of proper maps using filters In the beginning, you use $A$ when I think you mean $C$. Also, it is not clear to me what $\mathcal U_C$ is. May24 comment Characterization of proper maps using filters @PatrickDaSilva I believe I wanted to say that either $A$ or its complement is in $\mathcal U$. Sorry about that. May23 asked Characterization of proper maps using filters May23 accepted Dense implies strictly dense in TOP May23 comment Dense implies strictly dense in TOP I was thinking about proving that $\overline{O \cap X} = \bar O$. Looks like my thoughts were in the right direction. Thanks. May23 revised Dense implies strictly dense in TOP added 233 characters in body May23 asked Dense implies strictly dense in TOP May13 awarded Caucus Jan29 accepted Filters and sequences Jan29 asked Filters and sequences Dec4 comment Probability density function of $\sigma X + \mu$. Oops. Yeah, you guys are right. What I am wondering now is how you are dealing with the $\sigma < 0$ case. Dec4 comment How to prove these three norm equivalence problems These are matrix norms: en.wikipedia.org/wiki/Matrix_norm Dec4 comment Probability density function of $\sigma X + \mu$. For one thing, you expect that $\int_{\mathbb R} f_Z(x) \, dx = 1$, but if you use the formula for $f_Z(x)$ that you have, you don't get 1. Dec4 comment Poisson distribution and probability of random variables I am not understanding your problem. You have the formulas you need: just replace $\lambda$ with 5 and simplify.