As soon as I typed it out I thought of other baseses (what's the plural for this)?
Every basis though has to contain that basis so it will be uncountable. Is that right?
Prove that the discrete topology on an uncountable set does not satisfy the second axiom of countability.
The hint says: It is not enough to prove that one basis is uncountable but every basis is uncountable.
I can however only think of one possible basis and it's uncountable:
Is the hint misleading me?