  We introduce a topology ${\cal T}$ on the space $U$ of uniformly discrete
subsets of the Euclidean space. Assume that $S$ in $U$ admits a unique
autocorrelation measure. The diffraction measure of $S$ is purely atomic if and
only if $S$ is almost periodic in $(U,{\cal T})$. This result relates idealized
quasicrystals to almost periodicity. In the context of ergodic point processes,
the autocorrelation measure is known to exist. Then, the diffraction measure is
purely atomic if and only if the dynamical system has a pure point spectrum. As
an illustration, we study deformed model sets.
