Description:
AbstractA Σ‐group is an abelian group in which certain infinite sums are postulated to exist and to satisfy axioms suggested by the properties of unconditional sums in abelian convergence groups. Two notions of convergence are considered: in terms of nets, and in terms of filters. It is proved that every Σ‐group can be regarded as a net convergence group (of a particular type). An example is given to show that the same does not remain true if filters are used instead of nets. For the special class of ‘adic’ Σ‐groups, however, it is proved that filters are adequate.