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  • 1 The University of Oklahoma Norman, Oklahoma, 73019 USA
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Abstract  

Let S be an orthogonal polygon in the plane. Assume that S is starshaped via staircase paths, and let K be any component of Ker S, the staircase kernel of S, where KS. For every x in S\K, define WK(x) = {s: s lies on some staircase path in S from x to a point of K}. There is a minimal (finite) collection W(K) of WK(x) sets whose union is S. Further, each set WK(x) may be associated with a finite family UK(x) of staircase convex subsets, each containing x and K, with ∪{U: U in UK(x)} = WK(x). If W(K) = {WK(x1), ..., WK(xn)}, then KVK ≡ ∩{U: U in some family UK(xi), 1 ≤ in} ⊆ Ker S. It follows that each set VK is staircase convex and ∪{Vk: K a component of Ker S} = Ker S. Finally, if S is simply connected, then Ker S has exactly one component K, each set WK(xi) is staircase convex, 1 ≤ in, and ∩{Wk(xi): 1 ≤ i ≤ n} = Ker S.

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