6,301 reputation
1330
bio website jvanname.myweb.usf.edu
location Nowhere, Antarctica.
age 24
visits member for 2 years, 4 months
seen 18 mins 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.


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 $U$?
added 4 characters in body
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?
added 1289 characters in body
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
deleted 6 characters in body