Almost periodic functions in a group. I

Abstract

The numbers in brackets refer to the bibliography at the end of the paper. * That is, a topological set in the sense of Hausdorff [13,. One may take his topological system based on the notion of a neighborhood by means of Axioms 1, 2, 3 (or A, B, C) and one of the "separation" Axioms 4-8, such as 5. Furthermore, certain continuity assumptions have to be made concerning ab and a-1. In Parts I-III we shall need no topology at all, in Part IV we must assume that ab is continuous in a for fixed b and in b for fixed a, and in Part V we must assume that ab is continuous in (a, b) and that a-1 is continuous in a.