A closed (n + 1)-convex set in R2 is a union of n6 convex sets

M. A. Perles; S. Shelah

doi:10.1007/BF02801466

A closed (n + 1)-convex set in R² is a union of n⁶ convex sets

M. A. Perles^*
, S. Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

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

13 Scopus citations

Abstract

It is shown that if a closed set S in the plane is (n+1)-convex, then it has no more than n⁴ holes. As a consequence, it can be covered by≤n⁶ convex subsets. This is an improvement on the known bound of 2ⁿ·n³.

Original language	English
Pages (from-to)	305-312
Number of pages	8
Journal	Israel Journal of Mathematics
Volume	70
Issue number	3
DOIs	https://doi.org/10.1007/BF02801466
State	Published - Oct 1990

Access to Document

10.1007/BF02801466

Cite this

@article{414086f615114e14b4487649df0cf3f8,

title = "A closed (n + 1)-convex set in R2 is a union of n6 convex sets",

abstract = "It is shown that if a closed set S in the plane is (n+1)-convex, then it has no more than n4 holes. As a consequence, it can be covered by≤n6 convex subsets. This is an improvement on the known bound of 2n·n3.",

author = "Perles, \{M. A.\} and S. Shelah",

year = "1990",

month = oct,

doi = "10.1007/BF02801466",

language = "אנגלית",

volume = "70",

pages = "305--312",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - A closed (n + 1)-convex set in R2 is a union of n6 convex sets

AU - Perles, M. A.

AU - Shelah, S.

PY - 1990/10

Y1 - 1990/10

N2 - It is shown that if a closed set S in the plane is (n+1)-convex, then it has no more than n4 holes. As a consequence, it can be covered by≤n6 convex subsets. This is an improvement on the known bound of 2n·n3.

AB - It is shown that if a closed set S in the plane is (n+1)-convex, then it has no more than n4 holes. As a consequence, it can be covered by≤n6 convex subsets. This is an improvement on the known bound of 2n·n3.

UR - https://www.scopus.com/pages/publications/51249174598

U2 - 10.1007/BF02801466

DO - 10.1007/BF02801466

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:51249174598

SN - 0021-2172

VL - 70

SP - 305

EP - 312

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 3

ER -

A closed (n + 1)-convex set in R² is a union of n⁶ convex sets

Abstract

Access to Document

Other files and links

Fingerprint

Cite this