  We prove a general clustering result for the fractional Sobolev space
$W^{s,p}$: whenever the positivity set of a function $u$ in a square has
measure bounded from below by a multiple of the cube's volume, and the
$W^{s,p}$-seminorm of $u$ is bounded from above by a convenient power of the
cube's side, then $u$ is positive in a universally reduced cube. Our result
aims at applications in regularity theory for fractional elliptic and parabolic
equations. Also, by means of suitable interpolation inequalities, we show that
clustering results in $W^{1,p}$ and $BV$, respectively, can be deduced as
special cases.
