  In this paper we present a new semidefinite programming hierarchy for
covering problems in compact metric spaces. Over the last years, these kind of
hierarchies were developed primarily for geometric packing and for energy
minimization problems; they frequently provide the best known bounds. Starting
from a semidefinite programming hierarchy for the dominating set problem in
graph theory, we derive the new hierarchy for covering and show some of its
basic properties: The hierarchy converges in finitely many steps, but the first
level collapses to the volume bound when the compact metric space is
homogeneous.
