Not sure where to put a question about topology, but I'll try here. I'm trying to show that a certain topology for the Real line is not normal. The topology in question has no disjoint open sets (they are all nested) and therefore, no disjoint closed sets. If a topology has no disjoint closed sets, can it still be normal? I'd say not, but the only definition I have for normal requires me to start with disjoint closed sets, which in this case is impossible. Another possible approach... I've been able to show that the topology in question is not Hausdorff. Does that necessarily mean it is not normal? Any help is appreciated.