  Recent theoretical and experimental studies of superfluid $^3$He in aerogels
with a global anisotropy, e.g., due to an external stress, have definitely
shown that the A-like phase with an equal spin pairing (ESP) in such aerogel
samples is in the ABM (or, axial) pairing state. In this paper, the A-like
phase of superfluid $^3$He in globally {\it isotropic} aerogel is studied in
details by assuming a weakly disordered system in which singular topological
defects are absent. Through calculation of the free energy, a disordered ABM
state is found to be the best candidate of the pairing state of the globally
isotropic A-like phase. Further, it is found through a one-loop renormalization
group calculation that the coreless continuous vortices (or, vortex-skyrmions)
are irrelevant to the long-distance behavior of the disorder-induced textures,
and that the superfluidity is maintained in spite of lack of the conventional
off-diagonal long range order. Therefore, the globally isotropic A-like phase
at weak disorder is, like in the case with a global stretched anisotropy, a
superfluid glass with the ABM pairing.
