Achievement sets of conditionally convergent series
Volume 152 / 2018
Colloquium Mathematicum 152 (2018), 235-254 MSC: Primary 40A05; Secondary 11K31. DOI: 10.4064/cm7052-4-2017 Published online: 26 February 2018
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.