Which field of mathematics does Brouwer's Fixed Point Theorem belong to? Forgive me for asking a seemingly stupid question: Is Brouwer's Fixed Point Theorem an Analysis theorem, or a Topology theorem?
It's talking about functions so I assume it's part of Analysis. But Wikipedia says it's a theorem in Topology.
A follow-up question is, if I want to study something like Brouwer's Theorem in future, could you suggest me a specific branch of mathematics? eg. a specific branch in Algebraic Topology or Functional Analysis, something like that. (I'm not sure if these fields are related to this theorem, I'm just trying to give examples)
p.s. I've just started my undergraduate year 2 and not even Point-Set Topology has been taught. So forgive me if it seems that I have a lack of mathematical knowledge.

Branches of mathematics don't exist, there's no such thing, they're made up categories. Analysis and topology are closely related and Brouwer's fixed point theorem is a place where they meet and this is not a problem.
