6,651 reputation
1533
bio website jvanname.myweb.usf.edu
location Nowhere, KS
age 24
visits member for 2 years, 5 months
seen 1 hour ago

I am interested in to varying degrees ordered sets, general topology, point-free topology, set-theory, universal algebra, and model theory. Most of my mathematics research involves dualities that are similar to Stone duality. Yes. That is a real lightsaber in my profile picture.


1d
awarded  Nice Answer
1d
revised What is the maximal number of distinct values of the product of n permuted ordinals
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1d
answered What is the maximal number of distinct values of the product of n permuted ordinals
2d
awarded  Nice Answer
Aug
22
comment Ostaszewski space's construction Lemma
You don't need to use one of the special metrization theorems since we are dealing with locally compact spaces. In particular, a locally compact space is metrizable if and only if it can be written as a disjoint union of second countable spaces (this little result follows easily from the fact that metric spaces are paracompact and every paracompact locally compact space is a disjoint union of $\sigma$-compact spaces). Also, it does not seem too difficult to show that this space is a disjoint union of second countable spaces using the fact that $X$ space is locally compact and metrizable.
Aug
20
awarded  Good Answer
Aug
6
awarded  set-theory
Aug
5
comment non-Borel set which intersects every compact in a Borel set
I cannot immediately think of a a specific example of a non-Borel subset of $\omega_{1}$. However, the fact that $\mathcal{M}$ is a proper $\sigma$-algebra follows from the fact that the club filter is not an ultrafilter since no non-principal $\sigma$-complete ultrafilters appear until we reach the first measurable cardinal. In fact, Solovay's theorem states that $\omega_{1}$ can be partitioned into $\aleph_{1}$ stationary sets (and each element of this partition is non-Borel).
Aug
4
answered non-Borel set which intersects every compact in a Borel set
Jul
29
awarded  Pundit
Jul
29
comment Escape the zombie apocalypse
If the zombies can strategize, then regardless of how slow the zombies, walk the zombies can easily form a circle around you of a sufficiently large radius before you make it to the boundary of the circle so that whenever you cross from the inside of the circle to the outside of the circle, the zombies will be in a $d$ distance of you. All the zombies have to do is form a sequence of circles of radius say $2^{n}$ for all $n$ and the zombies are simply commanded to walk to the boundary of the nearest circle.
Jul
28
answered Locally compact Hausdorff space that is not normal
Jul
27
revised The word problem of the free left distributive algebra on one generator
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Jul
27
comment The word problem of the free left distributive algebra on one generator
Yes. These results can be proven in ZFC alone, and the Handbook of Set Theory outlines ZFC proofs of these results even though the proofs are not very set theoretical.
Jul
27
revised The word problem of the free left distributive algebra on one generator
added 7 characters in body
Jul
27
answered The word problem of the free left distributive algebra on one generator
Jul
18
comment Profinite completion of a partial order
Also, it seems as if the compactification that we are talking coincides with the Nachbin compactification. I gave an answer here mathoverflow.net/a/140625/22277 sketching basic facts about ordered topological spaces and I talked a little about the Nachbin compactification there. Also, Guram Bezhanishvili and Patrick Morandi both from New Mexico State University have written several relevant papers on partially ordered spaces and their ordered compactifications. The paper sierra.nmsu.edu/gbezhani/tos.pdf describes the Nachbin compactification and other ordered compactifications.
Jul
18
comment Profinite completion of a partial order
Yann Pequignot. You should post your proof as an answer to this question. Users are encouraged to answer their own questions if they find an answer after they ask the question.
Jul
18
awarded  Necromancer
Jul
17
answered Given A set $U$ and a set $\mathcal O$ of subsets of $U$, how many subsets of $\mathcal O$ have union $U$?