Elementary topical functions on b-complete semimodules over b-complete idempotent semifields

We extend some results of Rubinov and Singer [13] and Rubinov et al. [14] on topical functions on Rn and downward subsets of Rn to the case where Rn is replaced by a b-complete semimodule X over a b-complete idempotent semifield K. To this end, using residuation, we introduce “elementary” topical functions on X and we show that they are the “building blocks” of the set of all topical functions on X.