Dimensions of staircase kernels in orthogonal polygons |
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Authors: | Marilyn Breen |
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Institution: | (1) Department of Mathematics, University of Oklahoma, 73019 Norman, Oklahoma, U.S.A |
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Abstract: | LetS be a simply connected orthogonal polygon in the plane. If every four points ofS see (via staircase paths inS) a common segment, then the staircase kernel ofS contains a segment as well. A parallel result holds when every four points ofS see (via staircase paths inS) a common 2-dimensional set. In each case, the number 4 is best possible. However, both results fail without the requirement that setS be simply connected.An example shows that no Helly-type analogue is possible for intersections of orthogonally convex sets in the plane. |
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