bio | website | jvanname.myweb.usf.edu |
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location | Nowhere, Antarctica. | |
age | 24 | |
visits | member for | 2 years, 4 months |
seen | 18 mins ago | |
stats | profile views | 2,361 |
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.
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 |
Jul 7 |
reviewed | Reject suggested edit on nontrivial theorems with trivial proofs |
Jul 6 |
accepted | Is the monoid of taking iterated images and inverse images freely generated by the image and inverse image operation? |
Jul 6 |
asked | Is the monoid of taking iterated images and inverse images freely generated by the image and inverse image operation? |
Jul 5 |
answered | “countable” topology |
Jul 2 |
awarded | Curious |
Jul 2 |
answered | Homeomorphism between derived sets implies homeomorphism |
Jun 25 |
revised |
Finite lattices whose number of join-irreducibles does not exceed its height
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