  We investigate self-similar dynamical processes in an isothermal
self-gravitational fluid with spherical symmetry. In reference to earlier
complementary solution results of Larson, Penston, Shu, Hunter and Whitworth &
Summers, we further explore the `semi-complete solution space' from an initial
instant $t\to 0^{+}$ to a final stage $t\to +\infty$. These similarity
solutions can describe and accommodate physical processes of radial inflow,
core collapse, oscillations and envelope expansion (namely, outflow or wind) or
contraction as well as shocks. In particular, we present new classes of
self-similar solutions, referred to as `envelope expansion with core collapse'
(EECC) solutions, that are featured by an interior core collapse and an
exterior envelope expansion concurrently. The interior collapse towards the
central core approaches a free-fall state as the radius $r\to 0$, while the
exterior envelope expansion gradually approaches a constant radial flow speed
as $r\to +\infty$. There exists at least one spherical stagnation surface of
zero flow speed that separates the core collapse and the envelope outflow and
that travels outward at constant speed, either subsonically or supersonically,
in a self-similar manner.
