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## Some exercises

Algebraic Topology
Papapetros Vaggelis
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### Some exercises

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.