  Hydrodynamical calculations in three space dimensions of the collapse of an
isothermal, centrally condensed, rotating 1 M\sol protostellar cloud are
presented. A numerical algorithm involving nested subgrids is used to resolve
the region where fragmentation occurs in the central part of the protostar. A
previous calculation by Boss, which produced a hierarchical multiple system, is
evolved further, at comparable numerical resolution, and the end result is a
binary, with more than half of the mass of the original cloud, whose orbital
separation increases with time as a result of accretion of high-angular
momentum material and as a result of merging with fragments that have formed
farther out. Repeating the calculation with significantly higher resolution, we
find that a sequence of binaries can be induced by fragmentation of
circumbinary disks. The stability of the resulting multiple system is
investigated Using $n$-body calculations, which indicate that such a system
would transform on a short time scale into a more stable hierarchical
structure. The outermost and most massive binary which forms in the
high-resolution run has properties similar to that of the binary found in the
low-resolution calculation. Thus the basic outcome is shown to be independent
of the numerical spatial resolution. The high-resolution run, in addition,
leads to the formation of a system of smaller fragments, which might be
important for the understanding of the origin of close binaries with low-mass
components and of low mass single stars.
