Timeline for Functorial description of irreducibility of topological space?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 17, 2017 at 18:37 | comment | added | MTyson | You could try to find a similar categorical description of the space $T$ with elements $\{x,y,z\}$ and nontrivial closed sets $\{x,y\}$, $\{y,z\}$, and $\{y\}$. Then maps $f:X\to T$ with $x$ and $z$ in the image indicate that $f^{-1}(\{x,y\})$ and $f^{-1}(\{y,z\})$ are proper closed subsets covering $X$. | |
| Aug 17, 2017 at 2:54 | comment | added | Tim Campion | Martin Brandenburg points out that there's a "brute force" categorical characterization of the Sierpinski space. From there, you can talk about closed sets categorically and so also irreducibility. But somehow this is not terribly satisfying. | |
| Aug 16, 2017 at 22:54 | comment | added | David Roberts♦ | By the way, I wish I could +1 your user page, handy code and all. | |
| Aug 16, 2017 at 22:50 | comment | added | David Roberts♦ | Maybe in terms of the corresponding locale? Just a thought... | |
| Aug 16, 2017 at 21:13 | history | asked | Arrow | CC BY-SA 3.0 |