8,086 reputation
1835
bio website jvanname.myweb.usf.edu
location Gotham, NY
age 25
visits member for 2 years, 10 months
seen 4 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.


6h
answered Cohen algebra (generalization)
2d
comment zero-dimensional completely regular space with $\sigma$-complete clopen algebra
I also found that the paper Frolik's theorem for basically disconnected spaces by Johannes Vermeer it is also claimed that the basically disconnected spaces are precisely the zero-dimensional spaces $X$ where the Boolean algebra of all clopen sets is $\sigma$-complete as a Boolean algebra. I however have not seen a proof yet, so I do not believe this claim.
Jan
23
comment Approximating an arbitrary $\sigma$-algebra by simpler $\sigma$-algebras
For example, every partition of a complete Boolean algebra is a complete partition. Furthermore, under the refinement ordering, the complete partitions are closed under finite meets they are upwards closed. In other words, the complete partitions form a filter on the meet-semilattice of partitions of a Boolean algebra.
Jan
23
comment Approximating an arbitrary $\sigma$-algebra by simpler $\sigma$-algebras
Stefan. Besides representing Boolean algebras in terms of direct limits of power set algebras, there are nice ways to represent Boolean algebras in terms of products. A partition $p$ of a Boolean algebra $B$ is said to be a complete partition if whenever $c_{a}\leq a$ for each $a\in p$ the least upper bound $\bigvee_{a\in p}c_{a}$ exists. The complete partitions are precisely the partitions where the mapping $B\rightarrow\prod_{a\in p}B\upharpoonright a$ is an isomorphism of Boolean algebras. In fact, any decomposition of a Boolean algebra into a product is a decomposition of this form.
Jan
23
revised Approximating an arbitrary $\sigma$-algebra by simpler $\sigma$-algebras
added 1855 characters in body
Jan
23
answered Approximating an arbitrary $\sigma$-algebra by simpler $\sigma$-algebras
Jan
23
comment Characterizations of an exotic measure on the open sets in the circle $S^{1}$
Jochen Wengenroth. I fixed the definition of $\mu_{n}$. I apologize for the typo.
Jan
23
revised Characterizations of an exotic measure on the open sets in the circle $S^{1}$
added 5 characters in body
Jan
23
revised Characterizations of an exotic measure on the open sets in the circle $S^{1}$
added 75 characters in body; edited title
Jan
23
asked Characterizations of an exotic measure on the open sets in the circle $S^{1}$
Jan
20
comment Paracompact zero-dimensional space without clopen partition refinement
Ramiro de la Vega. Thanks for pointing that out. I corrected that typo.
Jan
20
revised Paracompact zero-dimensional space without clopen partition refinement
added 5 characters in body
Jan
19
comment Limits of conjugated subgroups
Johannes Hahn. I changed the answer so that it actually answers the question now.
Jan
19
revised Limits of conjugated subgroups
added 29 characters in body
Jan
19
comment Limits of conjugated subgroups
I guess I misread the question.
Jan
19
answered Limits of conjugated subgroups
Jan
19
answered Paracompact zero-dimensional space without clopen partition refinement
Jan
17
revised generalizing the ultrapower
I added information and I rewrote the latex so that the latex shows up properly.
Jan
17
asked Is it possible that all ultrafilters are determined by the meet-semilattice of sub-ultrapowers?
Jan
16
comment A categorical method to, say, determine the cardinality of a group
Arturo Magadin. I meant to say that from the epimorphisms one recovers the lattice of all normal subgroups instead of all subgroups.