  Let $X$ be a suitable function space and let $\cG \subset X$ be the set of
divergence free vector fields generating a global, smooth solution to the
incompressible, homogeneous three dimensional Navier-Stokes equations. We prove
that a sequence of divergence free vector fields converging in the sense of
distributions to an element of $\cG$ belongs to $\cG$ if $n$ is large enough,
provided the convergence holds "anisotropically" in frequency space. Typically
that excludes self-similar type convergence. Anisotropy appears as an important
qualitative feature in the analysis of the Navier-Stokes equations; it is also
shown that initial data which does not belong to $\cG$ (hence which produces a
solution blowing up in finite time) cannot have a strong anisotropy in its
frequency support.
