  If $(X,d)$ is a Polish metric space of dimension $0$, then by Wadge's lemma,
no more than two Borel subsets of $X$ can be incomparable with respect to
continuous reducibility. In contrast, our main result shows that for any metric
space $(X,d)$ of positive dimension, there are uncountably many Borel subsets
of $(X,d)$ that are pairwise incomparable with respect to continuous
reducibility.
  The reducibility that is given by the collection of continuous functions on a
topological space $(X,\tau)$ is called the \emph{Wadge quasi-order} for
$(X,\tau)$. We further show that this quasi-order, restricted to the Borel
subsets of a Polish space $(X,\tau)$, is a \emph{well-quasiorder (wqo)} if and
only if $(X,\tau)$ has dimension $0$, as an application of the main result.
  Moreover, we give further examples of applications of the technique, which is
based on a construction of graph colorings.
