  In the context of the relaxation time approximation to Boltzmann transport
theory, we examine the behavior of the Hall number, $n_H$, of a metal in the
neighborhood of a Lifshitz transition from a closed Fermi surface to open
sheets. We find a universal non-analytic dependence of $n_H$ on the electron
density in the high field limit, but a non-singular dependence at low fields.
The existence of an assumed nematic transition produces a doping dependent
$n_H$ similar to that observed in recent experiments in the high temperature
superconductor YBa$_2$Cu$_3$O$_{7-x}$.
