A topological construction of a non-smooth model of cumulativity

To solve a problem posed by Bezzazi, Makinson and Pérez, we construct an injective, non-smooth preferential structure validating cumulativity and weak determinacy, in which negation rationality fails. Essential use is made of infinite sequences of models approaching sets of models. To the author's knowledge, this is the first time that such topological constructions have been used in the context of preferential structures.