/sci/ - Science & Math

>>11530931
>More generally, is any subgroup of a compact Lie group also compact?
Nah, unless I've forgotten everything. Take the 2-torus [math]T = \mathbb{R}^2 / \mathbb{Z}^2[/math], choose your favorite [math](a, b)[/math] with [math]a/b \neq \mathbb{Q}[/math], let it generate a subgroup. Dense subset of the torus, wasn't it? Not closed, thus not compact.
There's probably a shitty analogous example for [math]SU(2)[/math].