Staircase kernels

Evelyn Magazanik; Micha A. Perles

doi:10.1515/ADVGEOM.2008.005

Staircase kernels

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

Let S ℝ² be a compact staircase connected set with stdiam(S) = n. In [4] we showed that Ker_r(S) is nonempty if r ≥ n+1/2 , and for r ≥ n/2 +1, er_r(S) is staircase connected. In this paper we determine the possible values of the staircase diameter of Ker _r(S) for r ≥ n/2 +1, and present interesting facts about Ker _r(S) when r = n/2 and r = n+1/2.

Original language	English
Pages (from-to)	87-100
Number of pages	14
Journal	Advances in Geometry
Volume	8
Issue number	1
DOIs	https://doi.org/10.1515/ADVGEOM.2008.005
State	Published - Apr 2008

Keywords

Staircase connectivity
Staircase kernels

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abstract = "Let S ℝ2 be a compact staircase connected set with stdiam(S) = n. In [4] we showed that Kerr(S) is nonempty if r ≥ n+1/2 , and for r ≥ n/2 +1, err(S) is staircase connected. In this paper we determine the possible values of the staircase diameter of Ker r(S) for r ≥ n/2 +1, and present interesting facts about Ker r(S) when r = n/2 and r = n+1/2.",

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AB - Let S ℝ2 be a compact staircase connected set with stdiam(S) = n. In [4] we showed that Kerr(S) is nonempty if r ≥ n+1/2 , and for r ≥ n/2 +1, err(S) is staircase connected. In this paper we determine the possible values of the staircase diameter of Ker r(S) for r ≥ n/2 +1, and present interesting facts about Ker r(S) when r = n/2 and r = n+1/2.

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Staircase kernels

Abstract

Keywords

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