6,376 reputation
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bio website jvanname.myweb.usf.edu
location Nowhere, KS
age 24
visits member for 2 years, 4 months
seen 2 hours 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.


1h
awarded  Pundit
3h
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.
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answered Locally compact Hausdorff space that is not normal
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revised The word problem of the free left distributive algebra on one generator
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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.
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revised The word problem of the free left distributive algebra on one generator
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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 $U$?
Jul
17
revised Given A set $U$ and a set $\mathcal O$ of subsets of $U$, how many subsets of $\mathcal O$ have union $U$?
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Jul
17
comment Profinite completion of a partial order
I would guess that the profinite completion of a partial order is a sort of generalized Stone Cech compactification of the partially ordered set $P$. More specifically, if $P$ is a poset, then let $\mathcal{L}(P)$ be the collection of all downwards closed subsets of $P$. Then let $\iota:P\rightarrow 2^{\mathcal{L}(P)}$ be the mapping where $\iota(x)(L)=1$ iff $x\in L$. Then let $X=\overline{\iota[P]}$. Then $X$ becomes a Priestley space with its natural partial ordering and it seems like $X$ is the profinite completion of $P$.
Jul
13
awarded  Enlightened
Jul
12
comment Almost everywhere in a rectangle
See mathoverflow.net/q/160329/22277.
Jul
11
awarded  Nice Answer
Jul
11
revised Which sets occur as boundaries of other sets in topological spaces?
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Jul
11
answered Which sets occur as boundaries of other sets in topological spaces?
Jul
9
reviewed Approve suggested edit on A realcompact analogue of the Baire category theorem
Jul
9
answered A realcompact analogue of the Baire category theorem