TITLE: Topological Group $G$ totally disconnected $\Rightarrow$ $G$ hausdorff?
QUESTION [5 upvotes]: On Wikipedia, I read that a topological group is necessarily Hausdorff if it is totally disconnected. Is that true? 
I read it on this page:
http://en.wikipedia.org/wiki/Totally_disconnected_group
If not, does anyone has an example for a totally disconnected group, which is not Hausdorff?
Thanks for help.

REPLY [5 votes]: A space $X$ is Hausdorff if and only if the diagonal $\Delta \subseteq X \times X$ is closed. In the case of a topological group, the diagonal can be described as the preimage of $\{1\}$ under the map $X\times X \to X : (x, y) \mapsto xy^{-1}$, and a point is closed in a disconnected space.