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Dec
3
accepted Sample space of the Monty Hall problem
Dec
2
asked Sample space of the Monty Hall problem
Sep
13
comment Finding the mean and Std Dev from Geometric probability
Just use the formula for P(X = x) in the formula for mean and std. deviation and simplify.
Sep
13
comment a normed vector space is normed closed iff it is weakly closed.
This question seems to have been posted before: math.stackexchange.com/questions/449301/…
Aug
23
awarded  Yearling
Jun
30
accepted Finitely many non-convergent ultrafilters
Jun
30
comment Finitely many non-convergent ultrafilters
Thanks. As you can tell, my intuition of ultrafilters sucks. I find your explanation using $\beta X$ intuitive, except that I don't see how the neighborhoods in $\beta X$ relate back to the elements inside the ultrafilters.
Jun
30
asked Finitely many non-convergent ultrafilters
Jun
5
accepted Non-convergent ultrafilter on $[0,\infty)$
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.