Intersection of maximal orthogonally starshaped polygons
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Let S be a simply connected orthogonal polygon in \( R^2 \) and let P(S) denote the intersection of all maximal starshaped via staircase paths orthogonal subpolygons in S. Our result: if \( P(S)\ne \emptyset \), then there exists a maximal starshaped via staircase paths orthogonal polygon \( T\subseteq S \), such that \( KerT\subseteq KerP(S) \). As a corollary, P(S) is a starshaped (via staircase paths) orthogonal polygon or empty. The results fail without the requirement that the set S is simply connected.
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