ABSTRACT
Let ω be an open subset of 1R2 and let r be a closed subset of θω without isolated points. We say that ω is an open set with cut τ if Int(cJJ) has a Lipschitz-continuous boundary (in the Necas[8] sense) and there exists a finite family {u^, . . . ,ω ^ } of pairwise disjoint, connected, open subsets of ω with Lipschitz-continuous boundary such that ω = U^ZUt· (see Figure 1). In this case, we also say that the family {ω \, . . . , ^ m } represents r in ω. In many practical situations, the cut r is a collection of (possibly intersecting) polygonal lines.
