bio  website  jvanname.myweb.usf.edu 

location  Nowhere, KS  
age  24  
visits  member for  2 years, 5 months 
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stats  profile views  2,433 
I am interested in to varying degrees ordered sets, general topology, pointfree topology, settheory, 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.
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awarded  Nice Answer 
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revised 
What is the maximal number of distinct values of the product of n permuted ordinals
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answered  What is the maximal number of distinct values of the product of n permuted ordinals 
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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  settheory 
Aug 5 
comment 
nonBorel set which intersects every compact in a Borel set
I cannot immediately think of a a specific example of a nonBorel 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 nonprincipal $\sigma$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 nonBorel). 
Aug 4 
answered  nonBorel 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
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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 $U$? 