Author： Breen M.
Publisher： Springer Publishing Company
ISSN： 0046-5755
Source： Geometriae Dedicata, Vol.75, Iss.2, 1999-04, pp. : 177-186
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Abstract
Let S be an orthogonal polygon in the plane, S simply connected, and let k=2,3. Set S is a union of k sets starshaped via staircase paths if and only if for every F finite, F⊆ bdry S, there is a set G⊆ bdry S arbitrarily close to F and points si,1 ⩽ i⩽k, (depending on G) such that each point of G is clearly visible from some si. An analogous result holds for a union of 2 sets starshaped via &agr;-paths when S is a closed simply connected set in the plane. Each result is best possible.
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