Intersections of maximal staircase sets

Evelyn Magazanik; Micha A. Perles

doi:10.1007/s00022-007-1948-1

Intersections of maximal staircase sets

Evelyn Magazanik^*, Micha A. Perles

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A compact set S ℝ² 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.

Original language	English
Pages (from-to)	127-133
Number of pages	7
Journal	Journal of Geometry
Volume	88
Issue number	1-2
DOIs	https://doi.org/10.1007/s00022-007-1948-1
State	Published - Mar 2008

Keywords

Orthogonal convexity
Staircase kernels
Staircase sets

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10.1007/s00022-007-1948-1

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AB - A compact set S ℝ2 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.

KW - Orthogonal convexity

KW - Staircase kernels

KW - Staircase sets

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Intersections of maximal staircase sets

Abstract

Keywords

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