  We introduce a uniform structure on any Hilbert $C^*$-module $\mathcal N$ and
prove the following theorem: suppose, $F:{\mathcal M}\to {\mathcal N}$ is a
bounded adjointable morphism of Hilbert $C^*$-modules over $\mathcal A$ and
$\mathcal N$ is countably generated. Then $F$ belongs to the Banach space
generated by operators $\theta_{x,y}$, $\theta_{x,y}(z):=x\langle y,z\rangle$,
$x\in {\mathcal N}$, $y,z\in {\mathcal M}$ (i.e. $F$ is ${\mathcal A}$-compact,
or "compact") if and only if $F$ maps the unit ball of ${\mathcal M}$ to a
totally bounded set with respect to this uniform structure (i.e. $F$ is a
compact operator).
