  Low-mass stars, those with main-sequence lifetimes that are of order the age
of the Universe, provide unique constraints on the Initial Mass Function (IMF)
when they formed. Star counts in systems with simple star-formation histories
are particularly straightforward to interpret, and those in old systems allow
one to determine the low-mass stellar IMF at large look-back times and thus at
high redshift. We present the faint stellar luminosity function (based on
optical HST data) in an external galaxy, the Ursa Minor dwarf Spheroidal
(dSph). This relatively-nearby (distance 70kpc) companion galaxy to the Milky
Way has a stellar population with narrow distributions of age and of
metallicity, remarkably similar to that of a classical halo globular cluster
such as M92 or M15, i.e. old and metal-poor. Contrasting with globular
clusters, the internal velocity dispersion of the Ursa Minor dSph indicates the
presence of significant amounts of dark matter. We find that the main sequence
stellar luminosity function of the Ursa Minor dSph, and implied IMF, down to
0.4 of a solar mass is indistinguishable from that of the halo globular
clusters M92 and M15. Thus the low mass stellar IMF for stars that formed at
high redshift is invariant in going from a low-surface-brightness,
dark-matter-dominated external galaxy, to a globular cluster within the Milky
Way.
