Consider the circle group T = R mod 2_ as the interval [0, 1). Then each x 2 T has a binary expansion: x =P1 k=1 xk2−k where each xk is 0 or 1. Let S be the set of x with a binary expansionsuch that the number of 1's does not exceed the number of the leading zeros by more than one. The authors prove that the countable compact set S cannot be expressed as the union of a finite number of Dirichlet sets.
D. E. Grow and M. Insall, "Further Properties of an Extremal Set of Uniqueness," Colloq. Math, American Mathematical Society, Jan 1998.
Mathematics and Statistics
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