DOIAbstract
AbstractErdős, Horváth and Joó discovered some years ago that for some real numbers 1<q<2 there exists only one sequence ci of zeroes and ones such that ∑ciq−i=1. Subsequently, the set U of these numbers was characterized algebraically in [P. Erdős, I. Joó, V. Komornik, Characterization of the unique expansions 1=∑q−ni and related problems, Bull. Soc. Math. France 118 (1990) 377–390] and [V. Komornik, P. Loreti, Subexpansions, superexpansions and uniqueness properties in non-integer bases, Period. Math. Hungar. 44 (2) (2002) 195–216]. We establish an analogous characterization of the closure U¯ of U. This allows us to clarify the topological structure of these sets: U¯∖U is a countable dense set of U¯, so the latter set is perfect. Moreover...
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