This paper represents a
continuing effort to develop elements of a general theory of packing and covering by
translates of a fixed subset of a group. For P a subset of a group X a subset L is a
left P-packing if for any distinct elements x1 and x2 in L, x1P ∩ x2P is empty. A
subset M of X is a left P-covering if MP = X. The Chabauty topology on the set of
discrete subgroups of a locally compact group has been used only to a rather limited
extent in the Geometry of Numbers but by its very definition is a natural one to work
with in studying packing and covering problems. The main results of this paper are
that the Chabauty topology extends to the family of all closed discrete subsets
containing the identity and that if X is σ-compact then S(X,P) the space
of all left P-packings for a fixed neighborhood P of the identity is locally
compact.
