7,831 reputation
1835
bio website jvanname.myweb.usf.edu
location Gotham, NY
age 25
visits member for 2 years, 9 months
seen 2 days 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.


2d
answered Do the mathematicians really know the exact values of what usually called “indeterminate forms”?
2d
comment Do the mathematicians really know the exact values of what usually called “indeterminate forms”?
In basic cardinal arithmetic one has $0\cdot\kappa=0,1^{\kappa}=1,0^{0}=1,\kappa^{0}=1$ for any infinite cardinal $\kappa$, so I guess $0\cdot\infty=0,1^{\infty}=1,0^{0}=1,\infty^{0}=1$ in this sense.
Dec
16
comment Universal and left-factoring order-preserving maps
@Dominic van der Zypen. Yes. I was thinking about using the proposition mentioned in this answer to construct a counterexample to the claim that the collection of universal maps is closed under composition. In particular, I was thinking about compositing a map satisfying the assumptions of the proposition with a map satisfying the assumptions of the dual of the proposition.
Dec
16
answered Universal and left-factoring order-preserving maps
Dec
13
awarded  Necromancer
Dec
13
answered Is the homomorphism poset directed if the codomain is directed?
Nov
15
revised Examples of algebras satisfying (a+b)(c+d)=ac+bd
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Nov
5
revised Natural associative law for a ternary “group”?
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Nov
5
comment Natural associative law for a ternary “group”?
I added a universal algebra tag since this question deals with very general algebraic structures of arity higher than two.
Nov
5
revised Natural associative law for a ternary “group”?
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Nov
5
answered Natural associative law for a ternary “group”?
Nov
1
revised The word problem of the free left distributive algebra on one generator
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Oct
20
comment Canonical functions in set theory and their applications
Also, the handbook of set theory page 99 refers to canonical functions as well along with other places.
Oct
20
comment Canonical functions in set theory and their applications
Canonical functions can also be found in Jech Ch. 24 Lem 24.5.
Oct
13
comment the meaning of “Cauchy filter” for an arbitrary topological group
The topological groups where the left uniformities and the right uniformities coincide are known as SIN (Small Invariant Neighborhood) groups. These are precisely the groups $G$ such that the identity $e$ has a basis consisting of sets $U$ such that $xUx^{-1}=U$ for all $x\in G$.
Oct
13
comment Homeo-Fixed point property
I suppose the fixed point property could also refer to $C^{r}$-maps on $C^{r}$-manifolds.
Oct
12
answered Homeo-Fixed point property
Oct
12
comment Why do roots of polynomials tend to have absolute value close to 1?
@Francois Dorais. I added to my answer some remarks that do explain why there should be rotational symmetry. Unfortunately it is not very rigorous at this point since the denominator could be near zero close to the contour. But I would agree that there is definitely more than meets the eye (just see Terry Tao's comments on my answer).
Oct
12
comment Why do roots of polynomials tend to have absolute value close to 1?
@Terry Tao. I have added a similar argument for why there should be rotational symmetry as well. Of course, this informal argument still suffers from the pesky fact that the denominator could be near zero. It seems like one could use the Poisson-Jensen Formula (for nearly arbitrary domains instead of simply the unit circle) for the pizza slice shaped domains to deduce rotational symmetry using $\log(|p(z)|)$ instead of $p'(z)/p(z)$. Is the usage of the Poisson-Jensen Formula for pizza slices the best way to formally rigorously deduce rotational symmetry or should different domains be used?
Oct
12
revised Why do roots of polynomials tend to have absolute value close to 1?
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