# Topology of the complex p-adic numbers

Let $\mathbb{Q}_p$, be the usual p-adic numbers, and then take the completion of its algebraic closure to get $\mathbb{C}_p$.

I was wondering if I could get a reference or some explanation as to what the topology on $\mathbb{C}_p$ is like?. I'm mainly interested in knowing if it is Hausdorff.

Thank you

-
Is it not a metric space ? –  Chandan Singh Dalawat Mar 13 at 15:58
...and Wikipedia gives references for that and related facts. –  Noah Stein Mar 13 at 16:05
It doesn't answer what you asked, but I thought you might enjoy this answer if you hadn't seen it already: mathoverflow.net/questions/51905/how-to-picture-mathbbc-p/… . –  Eric Peterson Mar 13 at 16:16
Unless I am missing something, it is homeomorphic to the Baire space $\omega^\omega$ (or $\mathbb R\smallsetminus\mathbb Q$, if you prefer), being the unique Polish zero-dimensional space with no nonempty compact open subset. –  Emil Jeřábek Mar 13 at 16:18
You could give a look at Robert's book "Introduction to $p$-adic analysis". But, as Dalawat said, it is metric, so Hausdorff... –  Filippo Alberto Edoardo Mar 13 at 16:45