Topology of univoque sets in real base expansions

Given a positive integer M and real number q∈(1,M+1], an expansion of x∈[0,M/(q−1)] over the alphabet A={0,1,…,M} is sequence (ci)∈AN such that x=∑i=1∞ciq−i. Generalizing many earlier results, we investigate in this paper topological properties set Uq consisting numbers x having unique form, combinatorial Uq′ their corresponding expansions. We also provide shorter proofs main results Baker [3] by adapting method given [12] for case M=1.