  Two graphs are of the same topological type if they can be mutually embedded
into each other topologically. We show that there are exactly $\aleph_1$
distinct topological types of countable trees. In general, for any infinite
cardinal $\kappa$ there are exactly $\kappa^+$ distinct topological types of
trees of size $\kappa$. This solves a problem of van der Holst from 2005.
