Abstract
AbstractTwo graphs are of the same topological type if they can be mutually embedded into each other topologically. We show that there are exactly $$\aleph _1$$
ℵ
1
distinct topological types of countable trees. In general, for any infinite cardinal $$\kappa $$
κ
there are exactly $$\kappa ^+$$
κ
+
distinct topological types of trees of size $$\kappa $$
κ
. This solves a problem of van der Holst from 2005.
Publisher
Springer Science and Business Media LLC