  We study star cluster formation in a low-metallicity environment using three
dimensional hydrodynamic simulations. Starting from a turbulent cloud core, we
follow the formation and growth of protostellar systems with different
metallicities ranging from $10^{-6}$ to $0.1~Z_{\odot}$. The cooling induced by
dust grains promotes fragmentation at small scales and the formation of
low-mass stars with $M_{*} \sim 0.01$--$0.1~M_{\odot}$ when $Z/Z_{\odot}
\gtrsim 10^{-5}$. While the number of low-mass stars increases with
metallicity, the stellar mass distribution is still top-heavy for $Z/Z_{\odot}
\lesssim 10^{-2}$ compared to the Chabrier initial mass function (IMF). In
these cases, star formation begins after the turbulent motion decays and a
single massive cloud core monolithically collapses to form a central massive
stellar system. The circumstellar disk preferentially feeds the mass to the
central massive stars, making the mass distribution top-heavy. When
$Z/Z_{\odot}=0.1$, collisions of the turbulent flows promote the onset of the
star formation and a highly filamentary structure develops owing to efficient
fine-structure line cooling. In this case, the mass supply to the massive stars
is limited by the local gas reservoir and the mass is shared among the stars,
leading to a Chabrier-like IMF. We conclude that cooling at the scales of the
turbulent motion promotes the development of the filamentary structure and
works as an important factor leading to the present-day IMF.
