In this note we develop some of the properties of separators of points in a
multiprojective space. In particular, we prove multigraded analogs of results
of Geramita, Maroscia, and Roberts relating the Hilbert function of X and X
\{P} via the degree of a separator, and Abrescia, Bazzotti, and Marino relating
the degree of a separator to shifts in the minimal multigraded free resolution
of the ideal of points.