Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom