Sorry if this question is below the level of this site: I've read that the quotient of a Hausdorff topological group by a closed subgroup is again Hausdorff. I've thought about it but can't seem to figure out why. Is it obvious? A simple yes or no (with reference is possible) is all I need.



Quotient of a Hausdorff topological group by a closed subgroup 
Edit: Below I expand my crude original answer "[Yes](http://en.wikipedia.org/wiki/Hausdorff_space)" as requested
by the community.




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Yes. Let $G$ be the group and $H$ be the closed subgroup. The [kernel](http://en.wikipedia.org/wiki/Kernel_of_a_function) of the quotient map $G \to G/H$ 
is equal to $\Delta^{-1}(H)$ where $\Delta : G \times G \to G$ 
is the continuous function $\Delta(x,y)= x- y$. Hence the kernel is closed. According
to [this](http://en.wikipedia.org/wiki/Hausdorff_space#Properties) $G/H$ is Hausdorff.


