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 Jun 5 comment Non-convergent ultrafilter on $[0,\infty)$ Well that was easy. Why do I complicate my life all the time... Jun 5 asked Non-convergent ultrafilter on $[0,\infty)$ Jun 5 awarded Informed May 27 accepted Characterization of proper maps using filters May 25 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 $f^{-1}(V) \subseteq O$? May 25 comment Characterization of proper maps using filters Of course! Thanks. May 25 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 $A$. May 24 revised Characterization of proper maps using filters added 779 characters in body May 24 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. May 24 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. May 24 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. May 23 asked Characterization of proper maps using filters May 23 accepted Dense implies strictly dense in TOP May 23 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. May 23 revised Dense implies strictly dense in TOP added 233 characters in body May 23 asked Dense implies strictly dense in TOP May 13 awarded Caucus Jan 29 accepted Filters and sequences Jan 29 asked Filters and sequences Dec 4 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.