Topology, functional analysis, and group theory

[-Alexander-]

Main Question or Discussion Point

What is the relationship between topology, functional analysis, and group theory? All three seem to overlap, and I can't quite see how to distinguish them / what they're each for.

 

[Bacle2]

I think the question is too broad as stated. Very generally, topology is about

continuity and about distinguishing spaces up to homeomorphisms, functional

analysis is about solving linear equations Lu=f in an infinite-dimensional context,

and group theory is about groups. Why don't you go over, say, Wikipedia and ask

something a little more narrow?