For an open covering U of a topological space and a mapping [InlineEquation not available: see fulltext.], where I:={(U,V)∈U×U;U∩V≠∅} , we present conditions for the existence of a mapping [InlineEquation not available: see fulltext.] satisfying C_V- C_U= d_UV for all (U, V) ∈ I . The result is applied to a Poincaré type theorem concerning distributional potentials. We also put the result into the context of algebraic topology.