bio  website  jvanname.myweb.usf.edu 

location  Gotham, NY  
age  25  
visits  member for  2 years, 10 months 
seen  4 hours ago  
stats  profile views  2,985 
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.
6h

answered  Cohen algebra (generalization) 
2d

comment 
zerodimensional 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 zerodimensional 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 meetsemilattice 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
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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 $S^{1}$
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Jan 23 
revised 
Characterizations of an exotic measure on the open sets in the circle $S^{1}$
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Jan 23 
asked  Characterizations of an exotic measure on the open sets in the circle $S^{1}$ 
Jan 20 
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Paracompact zerodimensional space without clopen partition refinement
Ramiro de la Vega. Thanks for pointing that out. I corrected that typo. 
Jan 20 
revised 
Paracompact zerodimensional space without clopen partition refinement
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Jan 19 
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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
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Jan 19 
comment 
Limits of conjugated subgroups
I guess I misread the question. 
Jan 19 
answered  Limits of conjugated subgroups 
Jan 19 
answered  Paracompact zerodimensional 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 meetsemilattice of subultrapowers? 
Jan 16 
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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. 