  The present work is devoted to an extension of the well-known Ehrling
inequalities, which quantitatively characterize compact embeddings of function
spaces, to more general operators. Firstly, a modified notion of continuity for
linear operators, named \emph{Ehrling continuity} and inspired by the classical
Ehrling inequality, is introduced, and then, a necessary and sufficient
condition for Ehrling continuity is provided via arguments based on general
topology. Secondly, general completely continuous operators between normed
spaces are characterized in terms of (generalized) Ehrling type inequalities.
To this end, the well-known local metrization of the weak topology (so to
speak, a \emph{very weak norm}) plays a crucial role. Thanks to these results,
a universal relation is observed among complete continuity, the very weak norm
and generalized Ehrling type inequality.
