Is This a Valid Topology on [0, ∞)?

[blahblah8724]

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!

 

[arkajad]

Given any nonepty set X, the collection (empty set, X) is a topology. It is called "trivial topology". Please, check that it indeed satisfies all the axioms of a topological space.

 

[AdrianZ]

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!

the intersection of (a,∞) and (b,∞) where a<b is (b,∞), not (a,b).