  Some filter relative notions of size, $\left( \mathcal{F},\mathcal{G}\right)
$-syndeticity and piecewise $\mathcal{F} $-syndeticity, were defined and
applied with clarity and focus by Shuungula, Zelenyuk and Zelenyuk in their
paper ``The closure of the smallest ideal of an ultrafilter semigroup.'' These
notions are generalizations of the well studied notions of syndeticity and
piecewise syndeticity. Since then, there has been an effort to develop the
theory around the algebraic structure of the Stone-\v{C}ech compactification so
that it encompasses these new generalizations. In this direction, we prove a
characterization of piecewise $\mathcal{F}$-syndetic sets. This fully answers a
conjecture of Christopherson and Johnson. arXiv:2105.09723
