10,184 reputation
12444
bio website jvanname.myweb.usf.edu
location Gotham, NY
age 25
visits member for 3 years, 2 months
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.


14h
comment Non-principal ultrafilters preserving infinite joins/meets
If the Boolean algebra $A$ is atomless then every ultrafilter $U$ is non-principal. In particular, any ultrafilter that preserves all those least upper bounds is a non-principal ultrafilter.
May
24
comment Uniform space structures of different metric on the same space
Prasit. Direct limits in the category of topological spaces are not very well behaved. For instance, the direct limit of completely regular spaces ("good spaces that one finds in analysis") could be non-Hausdorff ("a bad space").I would therefore not expect for these limits to be very well behaved. See for example cms.math.ca/openaccess/cmb/v12/cmb1969v12.0337-0338.pdf
May
24
comment Uniform space structures of different metric on the same space
As for the functor from metric spaces to uniform spaces, you should specify that morphisms you want to have between metric spaces since you could be asking for continuous maps, uniformly continuous maps, isometries, or Lipschitz continuous maps between metric spaces. If you are talking about uniformly continuous maps, take note that every complete uniform space is an inverse limit of complete uniform spaces with uniformly continuous transitional mappings.
May
24
comment Uniform space structures of different metric on the same space
Every finite $T_{1}$-space is discrete. Similarly, every finite separated uniform space is discrete since the diagonal is an entourage.
May
23
awarded  Nice Question
May
22
comment How long can a cycle of antichains in a finite partial order be?
domotorp. For a simple connected example better than $|X|+1$, take the tree $X=\{0,00,000,01,011,0111\}$ ordered by extension of strings, then the cycle in $\mathcal{A}_{X}$ containing $\emptyset$ has length 13.
May
21
revised How long can a cycle of antichains in a finite partial order be?
edited body
May
21
accepted When is a formula preserved under taking factors in a reduced product or the stalk in a Boolean product?
May
20
asked How long can a cycle of antichains in a finite partial order be?
May
17
comment Where does this strengthening of I1 stand?
I chose this axiomatization since the I1-tower cardinals are a modification to the notion of a Vopenka cardinal. Recall that a cardinal $\delta$ is a Vopenka cardinal if and only if whenever $A\subseteq V_{\delta}$ there is a $\kappa<\delta$ such that if $\kappa<\alpha<\delta$ there is some elementary embedding $j:\langle V_{\mu},\in,A\cap V_{\mu}\rangle\rightarrow\langle V_{\lambda},\in,A\cap V_{\lambda}\rangle$ with $\lambda,\mu<\delta$,$crit(j)=\kappa$, and $j(\kappa)>\alpha$. Therefore every I1-tower cardinal is a Vopenka cardinal and a limit of I1 cardinals.
May
17
comment Where does this strengthening of I1 stand?
Everett Piper. I simply wanted to extend the notion of an I1 cardinal to a larger cardinal with more consistency strength without resorting to models that necessarily look like L as one has with I0 cardinals, so I want to see what reasonable strengthenings of I1 are possible.
May
16
comment Where does this strengthening of I1 stand?
Victoria. Yes. That is what I meant. Thanks for pointing that out.
May
16
revised Where does this strengthening of I1 stand?
edited body
May
16
asked Where does this strengthening of I1 stand?
May
13
accepted Proving results about complete Boolean algebras in ZFC using Boolean valued models
May
11
comment In the category of uniform spaces, is the completion of a quotient map also a quotient map?
One problem with this definition of a quotient map that I have is that not every quotient map is surjective: if $Y$ is given the discrete uniformity, then function $f:X\rightarrow Y$ is automatically a quotient map since every map $g:Y\rightarrow Z$ is automatically continuous.
May
10
awarded  gn.general-topology
May
8
answered Mean on compact metric spaces
May
6
revised Zero-dimensional spaces and clopen separations
added 589 characters in body
May
6
comment Zero-dimensional spaces and clopen separations
For question 1, I am not immediately aware of any sources (besides my own) of this fact since the notion of an ultranormal space is not a well known notion. However, the proof that every normal strongly zero-dimensional space is ultranormal is easy and I have edited my answer to include such a proof.