Fundamental Group of Quotient Space

[James4]

Hi

I don't know how to attack the following question, any hints would be appreciated:

If G is a simply connected topological group and H is a discrete subgroup, then $\pi_1(G/H, 1) \cong H$.Thank you

James

 

[micromass]

Do you know how to find the fundamental group of $S^1$ (using covering spaces). Can you adjust the proof a little bit such that it holds in this case??