  Let K be a field that is complete with respect to a nonarchimedean absolute
value such that K has a countable dense subset. We prove that the Berkovich
analytification V^an of any d-dimensional quasi-projective scheme V over K
embeds in R^{2d+1}. If, moreover, the value group of K is dense in R_{>0} and V
is a curve, then we describe the homeomorphism type of V^an by using the theory
of local dendrites.
