Intersections of maximal staircase sets |
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Authors: | Evelyn Magazanik Micha A. Perles |
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Affiliation: | (1) Mathematics Department, The Hebrew University of Jerusalem, Edmond Safra Campus - Givat Ram, Jerusalem, Israel |
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Abstract: | A compact set is staircase connected if every two points a, b ∈ S can be connected by an x-monotone and y-monotone polygonal path with sides parallel to the coordinate axes. In [5] we have introduced the concepts of staircase k-stars and kernels. In this paper we prove that if the staircase k-kernel is not empty, then it can be expressed as the intersection of a covering family of maximal subsets of staircase diameter k of S. |
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Keywords: | 52A30 |
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