Recently I've been exploring probability measures on topological groups, derived from the (essentially) unique Haar measure defined thereon. I had begun to focus on the example of the circle group ...
I'm reading through Munkres and Armstrong's books on topology. However, I find topological groups to be really complicated objects! I feel they are twice as hard to deal with then just groups and ...
As I study more algebraic number theory, I hear more and more often about local compactness: locally compact fields, locally compact topological groups, Stone-Čech compactification of locally compact ...
Given any abstract group $ G $, how much is known about which types of topological/Lie group structures it might have? Any abstract group $ G $ will have the structure of a discrete topological group ...
A topology on a group is required to be compatible with the group structure (multiplication must be a continuous map $G\times G\to G$ and inversion must be continuous). I've only ever seen the ...
What are some interesting corollaries and consequences of the Pontryagin Duality theorem? My question can be taken as broadly as you'd like, even up to including any philosophy introduced specifically ...
I am coming to the end of a series of lecture notes on representations of $S_n$ and $GL(V)$. Near the end, it attempts to introduce the notion of the "character of a topological group", but doesn't ...