Further Properties of an Extremal Set of Uniqueness

David E. Grow, Missouri University of Science and Technology
Matt Insall, Missouri University of Science and Technology

This document has been relocated to http://scholarsmine.mst.edu/math_stat_facwork/673

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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.