Timeline for Inverse limit in metric geometry
Current License: CC BY-SA 2.5
17 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 1, 2012 at 13:38 | answer | added | Marc Palm | timeline score: 1 | |
| Mar 15, 2010 at 13:30 | answer | added | Jean Lecureux | timeline score: 2 | |
| Mar 1, 2010 at 5:00 | answer | added | Chad Groft | timeline score: 0 | |
| Feb 21, 2010 at 14:39 | answer | added | Pandelis Dodos | timeline score: 1 | |
| Feb 21, 2010 at 14:13 | comment | added | Anton Petrunin | @Henrik, in the paper I consider only compact metric spaces, nothing really irritating there... | |
| Feb 21, 2010 at 13:47 | comment | added | HenrikRüping | There is another irritating example: Consider the inverse system $X_n=\\{-n,\ldots,n\\}$ with distance $d(m,m')=|m-m'|$ and projections $\varphi_{n+1,n}:\\{-(n+1),\ldots,n+1\\}\rightarrow \\{-n,\ldots,n\\}$ defined by $\varphi_{n+1,n}(-n-1)=-n,\quad \varphi_{n+1,n}(n+1)=n,\quad \varphi_{n+1,n}|_{\\{-n,\ldots n\\}}=id$. Then the inverse limit is $\mathbb{Z}\cup\\{\pm \infty\\}$ and the metric is really just a quasimetric. | |
| Feb 21, 2010 at 13:20 | comment | added | HenrikRüping | I think the topology induced by the metric is not the inverse limit topology. But maybe this is no problem. It just irratated me. | |
| Feb 21, 2010 at 5:46 | comment | added | François G. Dorais | @Anton: OK. It was just a thought. I don't really know where the line is between MG and GT. I think that would be a good thing for me to know at some point. Why are continua GT and not MT? | |
| Feb 21, 2010 at 5:25 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Feb 21, 2010 at 4:48 | comment | added | Anton Petrunin | @François. Thank you, but no --- this is topology. @Tom. I add a "Why" in the question, which partly answers your question. | |
| Feb 21, 2010 at 4:47 | history | edited | Anton Petrunin | CC BY-SA 2.5 |
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| Feb 21, 2010 at 2:36 | comment | added | François G. Dorais | I don't know if it counts as MG per se, but I always liked this paper of Trevor Irwin and Slawek Solecki math.uiuc.edu/~ssolecki/papers/pseufraisfin.pdf | |
| Feb 21, 2010 at 2:04 | comment | added | Tom Leinster | Anton: as I understand it, "inverse system" means either functor from a cofiltered category, or functor from a (co)directed poset, according to taste (and then "inverse limit" means limit). Just to be clear, are you particularly interested in this special case of limits? Or are any types of limit of metric space interesting for you? | |
| Feb 21, 2010 at 1:58 | comment | added | Tom Leinster | Bill: yes . | |
| Feb 21, 2010 at 1:40 | comment | added | Bill Johnson | Short map = nonexpansive = Lipschitz constant at most one? | |
| Feb 21, 2010 at 1:33 | history | edited | Harald Hanche-Olsen | CC BY-SA 2.5 |
Spelling fix
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| Feb 21, 2010 at 0:52 | history | asked | Anton Petrunin | CC BY-SA 2.5 |