Take , , sets of . Since for all , then and now show that .
If you take the set and , what about ?
Show that the intersection of two topologies on the same set X is also a topology on X, but that their union may or may not be a topology.
I think this is way easier than i think. I have tied my mind in knots.
You need to check (T1-T3)
(T1) Obv from def of topology
I cannot see how to get (T3) to work