TITLE: Infinite Galois Theory
QUESTION [8 upvotes]: In infinite Galois theory for the one-one correspondence as in the finite case, one needs to introduce Krull topology. What is the intuition behind defining such topology ?

REPLY [8 votes]: Understand well the case of the infinite extension of the rationals generated by all $p$-the power roots of unity, where $p$ is a prime. Its Galois group is naturally isomorphic to the units in the $p$-adic integers. This unit group already comes equipped with the $p$-adic topology. Check that this topology really matches the Krull topology on the Galois side of things under the isomorphism between the Galois group and the $p$-adic units.