bio | website | jvanname.myweb.usf.edu |
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location | Gotham, NY | |
age | 25 | |
visits | member for | 3 years, 2 months |
seen | yesterday | |
stats | profile views | 3,353 |
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.
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 |
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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 |
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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 |
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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. |
May 5 |
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Zero-dimensional spaces and clopen separations
Pace Nielsen. You are correct. In my answer, I should have mentioned that ultranormality is the clopen separation property + $T_{1}$ (when dealing with normality and similar ideas I always assume the spaces are completely regular so that I do not have to deal with these issues). I edited my answer to address this issue. |