Péraire, Y., Infinitesimal approach to almost-automorphic functions, Annals of Pure and Applied Logic 63 (1993) 283–297. Thanks to the use of ideal elements of several levels, we are able to give a compact topological characterization of almost-automorphic functions. This new characterization turns out to be equivalent to a geometrical one: the existence of a relatively dense group of “pointwise periods”. However, the more significant result obtained, in our opinion, is a very important lowering of the complexity in characterizations and proofs.
