We study the family~$\cal B_0$ of the sets on which some
series of the form $\sum_{k\in\N}\left|\sin\pi n_kx\right|$
is uniformly bounded. We show that the families~$\cal B_0^c$
of all sets admitting the boundary~$c$ form a~hierarchy
which is incontinuous with respect to the operations of
intersection and union.
