Timeline for Can we generalize the result of Urysohn's lemma to countable collection of pairwise disjoint closed subsets of a normal space..?
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| Mar 17, 2013 at 21:40 | comment | added | David White | Another example is if you assign a sequence of values to the $A_n$ which doesn't converge (rather than converging to $\infty$), e.g. $1,-1,1,-1,...$. I don't think there's any hope for the kind of generalization you're asking for. | |
| Mar 17, 2013 at 20:34 | comment | added | Joseph Van Name | It still won't work even if you have constant value 1/n on $A_{n}$. | |
| Mar 17, 2013 at 20:12 | comment | added | Janson A.J | Actually that was a mistake that I said it takes constant value n on the nth set. Let's choose some bounded values, like 1/n.. | |
| Mar 17, 2013 at 19:36 | history | answered | David White | CC BY-SA 3.0 |