Does this form a topology?

1. blahblah8724

32
I am told that the interval (a, ∞) where a $\in$ (0, ∞) together the empty set and [0, ∞) form a topology on [0, ∞).

But I thought in a topology that the intersection if any two sets had to also be in the topology, but the intersection of say (a, ∞) with (b, ∞) where a<b is surely (a,b) which isn't in the topology?

Help! Thanks!