  By quenched-randomly mixing local units of different spatial
dimensionalities, we have studied Ising spin-glass systems on hierarchical
lattices continuously in dimensionalities 1 =< d =< 3. The global phase diagram
in temperature, antiferromagnetic bond concentration, and spatial
dimensionality is calculated. We find that, as dimension is lowered, the
spin-glass phase disappears to zero temperature at the lower-critical dimension
d_c=2.431. Our system being a physically realizable system, this sets an upper
limit to the lower-critical dimension in general for the Ising spin-glass
phase. As dimension is lowered towards d_c, the spin-glass critical temperature
continuously goes to zero, but the spin-glass chaos fully sustains to the brink
of the disappearance of the spin-glass phase. The Lyapunov exponent, measuring
the strength of chaos, is thus largely unaffected by the approach to d_c and
shows a discontinuity to zero at d_c.
