#### 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.)