  We prove that for any closed manifold of dimension 3 or greater that there is
an open set of smooth flows that have a hyperbolic set that is not contained in
a locally maximal one. Additionally, we show that the stabilization of the
shadowing closure of a hyperbolic set is an intrinsic property for
premaximality. Lastly,we review some results due to Anosov that concern
premaximality.
