  A packing of translates of a convex domain in the Euclidean plane is said to
be totally separable if any two packing elements can be separated by a line
disjoint from the interior of every packing element. This notion was introduced
by G. Fejes T\'oth and L. Fejes T\'oth (1973) and has attracted significant
attention. In this paper we prove an analogue of Oler's inequality for totally
separable translative packings of convex domains and then we derive from it
some new results. This includes finding the largest density of totally
separable translative packings of an arbitrary convex domain and finding the
smallest area convex hull of totally separable packings (resp., totally
separable soft packings) generated by given number of translates of a convex
domain (resp., soft convex domain). Finally, we determine the largest covering
ratio (that is, the largest fraction of the plane covered by the soft disks) of
an arbitrary totally separable soft disk packing with given soft parameter.
