What is the topological dimension of a (locally analytic) $p$-adic manifold over a non Archimedean field $K$?


Is the topological dimension of $K^n$, $n$?



Topological dimension of $p$-adic manifolds
$p$-adic numbers are locally compact, Hausdorff and totally disconnected (see this [nLab page](https://ncatlab.org/nlab/show/p-adic+number#Disconnectedness)), hence they are [zero-dimensional](https://en.wikipedia.org/wiki/Zero-dimensional_space). This means that---at least naively---topological dimension of $p$-adic manifolds doesn't work as you'd expect from real or complex manifolds. However, there are ways to do analytic geometry over the $p$-adic numbers, see e.g. [this stackexchange question](https://math.stackexchange.com/questions/581078/are-there-p-adic-manifolds) and the references on this [nLab page](https://ncatlab.org/nlab/show/non-archimedean+analytic+geometry).


