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Asymptotically Dense Dilations of Sets on the Circle
Author(s) -
Berend Daniel,
Peres Yuval
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-47.1.1
Subject(s) - sequence (biology) , mathematics , hausdorff distance , hausdorff space , property (philosophy) , metric (unit) , combinatorics , finite set , pure mathematics , discrete mathematics , mathematical analysis , epistemology , economics , biology , philosophy , operations management , genetics
Given an infinite closed subset A of the circle group T, we consider sequences of integers { n j } such that n j A → T in the Hausdorff metric. We prove the existence of a sequence of squares possessing this property and also a sequence of density 1. Quantitative versions for finite A are established as well.