I am a final year undergraduate student in Mathematics. I have a good background in algebra up to Galois theory of finite extensions of fields. I have started trying to understand the Galois theory of infinite extensions and here I get into some trouble. I am not familiar with topology at all. I have tried reading a bit myself but I am only aware of the very basic definitions. To be more specific, I don't have any "working experience" with topology - I know many of you will say this is unacceptable, but my University does not offer any courses on topology at all.
In particular, I can not understand what the phrase "endowed with the [some topology]". What does that really mean? Or phrases of the form "[some topology A] agrees with [some topology B]". This sort of situation appears in the definition of the topological Galois group of an infinite extension of fields. If I understand correctly, there is something called "the Krull topology" associated to the infinite Galois group, which is the inverse limit of Galois groups of finite extensions. I don't understand how this works.
Is there somewhere I can learn how to deal/understand the idea of topology in the context needed for Infinite Galois theory, or do I have to learn topology first from scratch. Thanks in advance for any help.