Completion and Regularization of Σ-Groups

Commutative groups in which also some infinite sums exist and interact compatibly with the finite ones were introduced by S. Wylie for use in algebraic topology and independently by Denis Higgs to develop an algebraic theory of integration. These "Σ-groups" admit suitable distinctions of completeness and regularity; here the question of completing, regularizing, and regularly completing such groups is treated.