On the topological structure of univoque sets

Erdos, Horvath and Joo discovered some years ago that for some real numbers 1 < q < 2 there exists only one sequence c(i) of zeroes and ones such that Sigma c(i) q(-i) = 1. Subsequently, the set U of these numbers was characterized algebraically in [P. Erdos, I. Joo, V. Komornik, Characterization of the unique expansions 1 = Sigma 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) over bar of U. This allows us to clarify the topological structure of these sets: (U) over bar U is a countable dense set of (U) over bar, so the latter set is perfect. Moreover, since U is known to have zero Lebesgue measure, (U) over bar is a Cantor set. (C) 2006 Elsevier Inc. All rights reserved.

On the topological structure of univoque sets / Vilmos, Komornik; Loreti, Paola. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - STAMPA. - 122:1(2007), pp. 157-183.



Titolo: On the topological structure of univoque sets
Autori: 
LORETI, Paola
mostra contributor esterni 
Data di pubblicazione: 2007
Rivista: 
JOURNAL OF NUMBER THEORY  
Citazione: On the topological structure of univoque sets / Vilmos, Komornik; Loreti, Paola. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - STAMPA. - 122:1(2007), pp. 157-183.
Handle: http://hdl.handle.net/11573/14218
Appartiene alla tipologia:01a Articolo in rivista

File allegati a questo prodotto
Non ci sono file associati a questo prodotto.
Utilizza questo identificativo per citare o creare un link a questo documento:
http://hdl.handle.net/11573/14218
  • Citazioni
  • PubMed Central ND
  • Scopus
  • WOS

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
 
 
 
Powered by IRIS-about IRIS-Utilizzo dei cookie
Logo CINECA  Copyright © 2021