Multigeometric sequences and Cantorvals

• Autorzy: Artur Bartoszewicz , Małgorzata Filipczak , Emilia Szymonik
• Języki publikacji: EN

Abstrakty

EN

For a sequence x ∈ l 1\c 00, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann [Guthrie J.A., Nymann J.E., The topological structure of the set of subsums of an infinite series, Colloq. Math., 1988, 55(2), 323–327] we describe families of sequences which contain, according to our knowledge, all known examples of x with E(x) being Cantorvals.

Słowa kluczowe

EN

Multigeometric sequence; Achievement set of sequence; M-Cantorval

Kategorie tematyczne

• 28A75: Length, area, volume, other geometric measure theory
• 40A05: Convergence and divergence of series and sequences
• 11B05: Density, gaps, topology

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 7
• Strony: 1000-1007

Daty

wydano

2014-07-01

online

2014-04-03

Twórcy

autor

Artur Bartoszewicz

• Technical University of Łódź

autor

Małgorzata Filipczak

• Łódź University

autor

Emilia Szymonik

• Technical University of Łódź

Bibliografia

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• [11] Nymann J.E., Sáenz R.A., The topological structure of the set of P-sums of a sequence, Publ. Math. Debrecen, 1997, 50(3–4), 305–316
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Identyfikatory

DOI

10.2478/s11533-013-0396-4