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#### The countable Erdös-Menger conjecture with ends

Erdös 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, for countable graphs~$G$,
the

extension of this conjecture in which $A,B$ and $X$ are allowed
to contain

ends as well as vertices, and where the closure of $A$ avoids
$B$ and vice

versa. (Without the closure condition the extended conjecture
is false.)

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