CONSTRUCTION OF ONE-DIMENSIONAL SUBSETS OF THE REALS NOT CONTAINING SIMILAR COPIES OF GIVEN PATTERNS

被引：29

作者：

Keleti, Tamas ^{[1
]}

机构：

[1] Eotvos Lorand Univ, Dept Anal, H-1117 Budapest, Hungary

来源：

ANALYSIS & PDE | 2008年 / 1卷 / 01期

关键词：

Hausdorff dimension; avoiding pattern; Erdos similarity problem; similar copy; affine copy;

D O I：

10.2140/apde.2008.1.29

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For any countable collection of sets of three points we construct a compact subset of the real line with Hausdorff dimension 1 that contains no similar copy of any of the given triplets.

引用

页码：29 / 33

页数：5

共 15 条

[1]

[Anonymous], 1990, FRACTAL GEOMETRY

[2]

BISBAS A, 2006, AVOIDING AFFIN UNPUB

[3] CONSTRUCTION OF SETS OF POSITIVE MEASURE NOT CONTAINING AN AFFINE IMAGE OF A GIVEN INFINITE STRUCTURE [J].

BOURGAIN, J .

ISRAEL JOURNAL OF MATHEMATICS, 1987, 60 (03) :333-344

[4] Covering R with translates of a compact set [J].

Darji, UB ;

Keleti, T .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (08) :2593-2596

[5] Less than 2ω many translates of a compact nullset may cover the real line [J].

Elekes, M ;

Steprans, J .

FUNDAMENTA MATHEMATICAE, 2004, 181 (01) :89-96

[6]

Erdos P., 1957, Colloq. Math., V4, P195

[7]

ERDOS P, 1974, MATH BALKANICA, V4, P197

[8] ON A PROBLEM OF ERDOS ON SEQUENCES AND MEASURABLE SETS [J].

FALCONER, KJ .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 90 (01) :77-78

[9] A visit to the Erdos problem [J].

Humke, PD ;

Laczkovich, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (03) :819-822

[10]

Keleti T., 1998, REAL ANAL EXCHANGE, V24, P843, DOI 10.2307/44153003

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