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
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.
