  Given an algebraic variety X defined over an algebraically closed field, we
study the space RZ(X,x) consisting of all the valuations of the function field
of X which are centered in a closed point x of X. We concentrate on its
homeomorphism type. We prove that, when x is a regular point, this
homeomorphism type only depends on the dimension of X. If x is a singular point
of a normal surface, we show that it only depends on the dual graph of a good
resolution of (X,x) up to some precise equivalence. This is done by studying
the relation between RZ(X,x) and the normalized non-Archimedean link of x in X
coming from the point of view of Berkovich geometry. We prove that their
behavior is the same.
