  Answering a question of Diestel, we develop a topological notion of gammoids
in infinite graphs which, unlike traditional infinite gammoids, always define a
matroid. As our main tool, we prove for any infinite graph $G$ with vertex sets
$A$ and $B$ that if every finite subset of $A$ is linked to $B$ by disjoint
paths, then the whole of $A$ can be linked to the closure of $B$ by disjoint
paths or rays in a natural topology on $G$ and its ends. This latter theorem
re-proves and strengthens the infinite Menger theorem of Aharoni and Berger for
`well-separated' sets $A$ and $B$. It also implies the topological Menger
theorem of Diestel for locally finite graphs.
