  We demonstrate the Parker Magnetostatic Theorem in terms of a small
neighborhood in solution space containing continuous force-free magnetic fields
in small deviations from the uniform field. These fields are embedded in a
perfectly conducting fluid bounded by a pair of rigid plates where each field
is anchored, taking the plates perpendicular to the uniform field. Those
force-free fields obtainable from the uniform field by continuous magnetic
footpoint displacements at the plates have field topologies that are shown to
be a restricted subset of the field topologies similarly created without
imposing the force-free equilibirum condition. The theorem then follows from
the deduction that a continuous nonequilibrum field with a topology not in that
subset must find a force-free state containing tangential discontinuities.
