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Achievement sets of conditionally convergent series

Volume 152 / 2018

Artur Bartoszewicz, Szymon Głąb, Jacek Marchwicki Colloquium Mathematicum 152 (2018), 235-254 MSC: Primary 40A05; Secondary 11K31. DOI: 10.4064/cm7052-4-2017 Published online: 26 February 2018

Abstract

Considering the sets of subsums of series (or achievement sets) we show that for conditionally convergent series the multidimensional case is much more complicated than that of the real line. Although we are far from the full topological classification of such sets, we present many surprising examples and capture the ideas standing behind them in general theorems.

Authors

  • Artur BartoszewiczInstitute of Mathematics
    Łódź University of Technology
    Wólczańska 215
    93-005 Łódź, Poland
    e-mail
  • Szymon GłąbInstitute of Mathematics
    Łódź University of Technology
    Wólczańska 215
    93-005 Łódź, Poland
    e-mail
  • Jacek MarchwickiInstitute of Mathematics
    Łódź University of Technology
    Wólczańska 215
    93-005 Łódź, Poland
    e-mail

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