This may be a stupid question.But I am stuck with it.Is Q\_p(the p-adic) connected under the usual topology?I was confounded with this problem while trying to construct a counter-example related to my master's thesis.



On topology of p-adic numbers.
Any non-empty open can be written as a disjoint union of opens ; for example
$\mathbb{Z}\_p=\cup(a+p\mathbb{Z}\_p)$ where $a$ runs through $\{0...(p-1)\}$. Those spaces are said totally disconnected.


