Timeline for Defining a topology in the Power Set
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Feb 26, 2015 at 10:13 | answer | added | Michał Masny | timeline score: 1 | |
| Sep 22, 2014 at 14:22 | history | edited | David White | CC BY-SA 3.0 |
Fixed typos
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| Aug 27, 2014 at 11:08 | comment | added | Hiro Lee Tanaka | Whatever topology you put on it, you should check whether the operation of union is continuous. If so, $2^T$ may well be contractible. (It'll be a topological, unital monoid where every element is idempotent.) | |
| Aug 27, 2014 at 10:56 | answer | added | Adam Epstein | timeline score: 11 | |
| Aug 27, 2014 at 9:29 | answer | added | Dominic van der Zypen | timeline score: 6 | |
| Aug 27, 2014 at 9:13 | comment | added | Lehs | Do the study of continuous functions on $2^X$-spaces totaly coincide with that of continuous relations? Or will the question of domain for the previous make a difference? | |
| Aug 27, 2014 at 8:41 | history | edited | Asaf Karagila♦ |
edited tags
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| Jun 7, 2013 at 7:46 | answer | added | Joseph Van Name | timeline score: 14 | |
| Jun 7, 2013 at 7:20 | comment | added | Adam Przeździecki | Usually not all of $2^T$ is considered but some interesting subsets. You may wish to look at the monograph S.B. Nadler "Hyperspaces of Sets" (1978), 707pp. | |
| Jun 7, 2013 at 6:50 | history | edited | Joseph Van Name |
I added the general topology tag.
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| Jun 7, 2013 at 6:35 | comment | added | Sergei Akbarov | A remark to the construction of Dan Ramras: it becomes much more interesting if you endow the two point space, let us denote it by $2=\{0,1\}$, with the connected topology, where $\{0\}$ is closed and $\{1\}$ is open. Then the pre-image of $\{0\}$ is closed in $T$, and the pre-image of $\{1\}$ is open. And the set $2^T$ of maps $f:T\to 2$ is in one-to-one correspondense with the set of all closed (/open) subsets in $T$, and you can endow $2^T$ with different interesting topologies. So actually, I think you should understand first, whether you need all subsets in $T$ or, say, just closed ones. | |
| Jun 7, 2013 at 5:07 | answer | added | Steven Landsburg | timeline score: 4 | |
| Jun 7, 2013 at 4:40 | comment | added | Dan Ramras | Well, you could think of $2^T$ as the set, or space, of maps from $T$ to a discrete two point space, with the compact-open topology. Of course this is not very interesting if $T$ is connected, and maybe still not very interesting in general. | |
| Jun 7, 2013 at 4:32 | history | asked | Joaquín Moraga | CC BY-SA 3.0 |