  For an open covering $\mathcal U$ of a topological space and a mapping
$d\colon\mathcal I\to\mathbb{K}$, where $\mathcal I:=\bigl\{(U,V)\in\mathcal
U\times\mathcal U;\ U\cap V\ne\varnothing\bigr\}$, we present a context for the
existence of a mapping $C\colon\mathcal U\to\mathbb{K}$ satisfying
$C_V-C_U=d_{UV}$ for all $(U,V)\in\mathcal I$. The result is applied to a
Poincar\'e type theorem concerning distributional potentials. We also put the
result into the context of algebraic topology.
