Let's suppose that (A, F) is a measurable space (A underlying set, F the sigma algebra), and that F arises from some topology T.
I would like a theorem of the form:
All singletons belong to F if and only if (A, F, T) has properties P1,P2,...
where P1,P2,... may be measure theoretic or topological conditions on the triple (A, T, F).
Thanks a lot for your help.