Abstract.
A compact set \(S \subset {\mathbb{R}}^{2}\) 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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Magazanik, E., Perles, M.A. Intersections of maximal staircase sets. J. geom. 88, 127–133 (2008). https://doi.org/10.1007/s00022-007-1948-1
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DOI: https://doi.org/10.1007/s00022-007-1948-1