Erd\"os conjectured that, given an infinite graph $G$
and vertex sets
$A,B\sub V(G)$, there exist a set $\P$ of disjoint $A$--$B$ paths
in $G$ and an
$A$--$B$ separator $X$ `on'~$\P$, in the sense that $X$ consists
of a choice of
one vertex from each path in~$\P$. We prove the conjecture for
vertex sets $A$
and $B$ that have disjoint closures in the usual topology on graphs
with ends.
The result can be extended by allowing $A$, $B$ and $X$ to contain
ends as
well as vertices.