  We investigate the nature of the AdS/CFT duality between a subregion of the
bulk and its boundary. In global AdS/CFT in the classical G_N=0 limit, the
duality reduces to a boundary value problem that can be solved by restricting
to one-point functions of local operators in the CFT. We show that the solution
of this boundary value problem depends continuously on the CFT data. In
contrast, the AdS-Rindler subregion cannot be continuously reconstructed from
local CFT data restricted to the associated boundary region. Motivated by
related results in the mathematics literature, we posit that a continuous bulk
reconstruction is only possible when every null geodesic in a given bulk
subregion has an endpoint on the associated boundary subregion. This suggests
that a subregion duality for AdS-Rindler, if it exists, must involve nonlocal
CFT operators in an essential way.
