Timeline for Do the empty set AND the entire set really need to be open?
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| Mar 25, 2010 at 3:30 | comment | added | Pete L. Clark | I just noticed something amusing in the above rather trivial claims. If you take T_1 to mean (as I did) that points are closed, then in the above world of non-automatic openness of $\emptyset$ and $X$, Hausdorff does not imply T_1: consider a one point space with non-open empty set! | |
| Mar 25, 2010 at 1:38 | comment | added | Qiaochu Yuan | Anything you can say in topology applies only to the union of all of the open sets in X. If there are points in X not in this union, they might as well not be there; in other words, I see no conceivable reason to exclude the entire set from being open. | |
| Mar 25, 2010 at 1:09 | history | answered | Pete L. Clark | CC BY-SA 2.5 |