Let be an algebraic (infinite) Galois extension with group .
We can define the Krull topology on the group .
We wish to show this topology is totally disconnected.
Let some subset of .
Then there exists a subgroup of the form where is a finite Galois extension with (this is just a property on how this topology is defined).
Thus, is a union of two non-empty open sets.
My question is why are those sets open?