Asymptotically Dense Dilations of Sets on the Circle Academic Article uri icon


  • 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.

publication date

  • January 1, 1993