  We prove that if a sequence of geodesically complete CAT$(0)$-spaces $X_j$
with uniformly cocompact discrete groups of isometries converges in the
Gromov-Hausdorff sense to $X_\infty$, then the dimension of the maximal
Euclidean factor splitted off by $X_\infty$ and $X_j$ is the same, for $j$ big
enough. In other words, no additional Euclidean factors can appear in the
limit.
