Some exercises
Posted: Tue Nov 10, 2015 12:24 pm
Let \(\displaystyle{\left(G,\cdot,\mathbb{T}\right)}\) be a topological group.
1. If \(\displaystyle{H}\) is a closed subgroup, then prove that \(\displaystyle{G/H}\) is a \(\displaystyle{\rm{Hausdorff}}\) topological space.
2. Each open subgroup is closed.
1. If \(\displaystyle{H}\) is a closed subgroup, then prove that \(\displaystyle{G/H}\) is a \(\displaystyle{\rm{Hausdorff}}\) topological space.
2. Each open subgroup is closed.