  We introduce the notion of pseudo-cones of metric spaces as a generalization
of both of the tangent cones and the asymptotic cones. We prove that the
Assouad dimension of a metric space is bounded from below by that of any
pseudo-cone of it. We exhibit a example containing all compact metric spaces as
pseudo-cones, and examples containing all proper length spaces as tangent cones
or asymptotic cones.
