So I came across something called "Topological Groups". I have just taken a course on topology/and some basic algebraic topology which i really liked. My mind was blown. I said topological groups are awesome. But then i thought ... are they still useful?
I heard general topology is dead but is it a branch of general topology or not?. Can they still provide usefulness to the other parts of math like harmonic analysis physics or pdes as i read they used to, or new methods for these problems have replaced topological groups.
So all these sum up to the following question ! What's the status on this subject (active or dead) and is it considered an area of research and what is it called?