The Erdös-Menger conjecture for source/sink sets with disjoint closures

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.

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