Timeline for Categorical Description of Open Subspaces
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| May 2, 2017 at 0:59 | comment | added | Colin | I think the Sierpinski space can also be defined as the lax pushout of $Id_1$ along itself. (Considering Top as a poset-enriched category where $Hom(X,Y)$ is ordered pointwise using the specialization order on $Y$). | |
| Apr 28, 2017 at 21:34 | comment | added | Martin Brandenburg | 1) Corrected. 2) Well we have to say which point is closed and which point is open. Notice that my first definition of a Sierpinski is completely symmetric. So it cannot be complete. 3) For $Top$ this is the case. | |
| Apr 28, 2017 at 2:37 | comment | added | Tim Campion | I'm confused by a few things in the answer you link to. 1) The codiscrete category with two elements meets your definition of a Sierpinski object (a connected object with two global points), but I don't see where you consider this. 2) I don't understand what you mean by "distinguishing two isomorphic Sierpinski spaces from each other". Do you mean you want to distinguish the two points $x,y: 1 \to S$ of the Sierpinski space $S$ from each other? 3.) You mention certain maps that do certain things to $y$; are you claiming there are no maps that do similar things to $x$? | |
| S Apr 27, 2017 at 22:40 | history | answered | Martin Brandenburg | CC BY-SA 3.0 | |
| S Apr 27, 2017 at 22:40 | history | made wiki | Post Made Community Wiki by Martin Brandenburg |