9,737 reputation
12343
bio website jvanname.myweb.usf.edu
location Gotham, NY
age 25
visits member for 3 years, 1 month
seen 6 hours ago

I am interested in to varying degrees ordered sets, general topology, point-free topology, Boolean algebras, set-theory, universal algebra, and model theory. Most of my mathematics research involves dualities that are similar to Stone duality.


2d
revised Lebesgue covering dimension for locales
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2d
answered Lebesgue covering dimension for locales
Apr
21
comment Two notions of zero-dimensionality for topological spaces
It turns out that one can get by with this result with subfitness which is a pointfree separation axiom which is weaker than $T_{1}$. We say that a frame $L$ is subfit if whenever $x\not\leq y$ there is some $c$ with $x\vee c=1\neq y\vee c$. In fact, if $L$ is a subfit frame such that if $x\vee y=1$, then there is some complemented element $a$ with $a\leq x,a'\leq y$, then $L$ has a basis of complemented elements.
Apr
21
comment Two notions of zero-dimensionality for topological spaces
zero-dimensionality+$T_{1}$ with respect to Lebesgue covering dimension is known as ultraparacompactness while zero-dimensionality with respect to small inductive dimension is commonly known as simply zero-dimensionality. See my answer at mathoverflow.net/a/134184/22277 for more information on the relation between ultraparacompactness and zero-dimensionality.
Apr
20
asked When is a formula preserved under taking factors in a reduced product or the stalk in a Boolean product?
Apr
19
comment Are all minimal totally separated spaces compact?
It looks like this question has been answered by Eric Wofsey here mathoverflow.net/a/203252/22277 in a similar question posted.
Apr
18
revised Counterexample on completely distributive lattices
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Apr
18
revised Counterexample on completely distributive lattices
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Apr
18
answered Counterexample on completely distributive lattices
Apr
9
comment Characterizing Inf and Sup sets
If you don't like writing $\textrm{Inf}(\leq)$, then you could write $\textrm{Inf}(X,\leq)$ instead. And writing $\textrm{Inf}(\leq)$ is not any more ambiguous than writing $\textrm{Inf}(R)$.
Apr
9
revised Convergent filters generated by (not necessarily countable) chains
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Apr
8
comment Characterizing Inf and Sup sets
user47958. Writing $(X,R)$ for a partially ordered set is not a standard practice. I do not recall ever seeing a mathematician use $R$ for a partial ordering relation. Usually one writes $\leq$ or maybe even $\preceq$ for a partially ordering.
Apr
8
answered Convergent filters generated by (not necessarily countable) chains
Apr
7
revised Is there some absoluteness between the Boolean valued universe $V^{B}$ and $V$?
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Apr
7
comment Is there some absoluteness between the Boolean valued universe $V^{B}$ and $V$?
I have edited this question. Now it should be much more answerable and clear what I am looking for.
Apr
7
revised Is there some absoluteness between the Boolean valued universe $V^{B}$ and $V$?
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Apr
7
awarded  Necromancer
Apr
7
answered Measure with `somewhere dense' support
Apr
7
answered Measure with `somewhere dense' support
Apr
5
revised Is there a compact connected Hausdorff space in which every non-empty $G_\delta$ set has non-empty interior?
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