Timeline for answer to Why is a topology made up of 'open' sets? by Qiaochu Yuan
Current License: CC BY-SA 2.5
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7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2012 at 2:06 | comment | added | Toby Bartels | I think that it's a mistake to say ‘and on the empty set’. The justification that $\emptyset$ is open (which is given in Qiaochu's last comment) is entirely different from the justification that $X$ is open. | |
| Jun 27, 2011 at 14:15 | history | made wiki | Post Made Community Wiki | ||
| Mar 24, 2010 at 21:36 | comment | added | Qiaochu Yuan | I guess another answer is that "arbitrary union" includes the empty union. | |
| Mar 24, 2010 at 21:33 | comment | added | LSpice | I think I am missing here why the empty set should be included. It is certainly intuitive that a property that has been checked on $X$ is true on $X$; but, if I were a student presented with this definition, then I'd wonder, I think not unreasonably, why I should check it on $\emptyset$ as well. | |
| Mar 24, 2010 at 12:45 | comment | added | Minhyong Kim | Qiaochu: I agree with your soapboxing comment. I've indicated my reasons somewhat in the recent edit. | |
| Mar 24, 2010 at 9:00 | comment | added | Kevin H. Lin | Re soapboxing: I also think the idea of a topological space must be deeper than "just" a generalization of metric spaces or of $\mathbb{R}$; this is one of the reasons for this previous question of mine: mathoverflow.net/questions/14634/… | |
| Mar 24, 2010 at 8:50 | history | answered | Qiaochu Yuan | CC BY-SA 2.5 |