The notion of a complete sequence of pairwise disjoint coanalytic sets is investigated. Several examples are given and such sequences are characterised under analytic determinacy. The ideas are based on earlier results of Saint Raymond, and generalise them.
A subobjects structure of the category - of -fuzzy sets over a complete -algebra is investigated, where an -fuzzy set is a pair such that is a set and is a special map. Special subobjects (called complete) of an -fuzzy set which can be identified with some characteristic morphisms are then investigated. It is proved that some truth-valued morphisms , are characteristic morphisms of complete subobjects.
Assume that no cardinal κ < 2ω is quasi-measurable (κ is quasi-measurable if there exists a κ-additive ideal of subsets of κ such that the Boolean algebra P(κ)/ satisfies c.c.c.). We show that for a metrizable separable space X and a proper c.c.c. σ-ideal II of subsets of X that has a Borel base, each point-finite cover ⊆ of X contains uncountably many pairwise disjoint subfamilies , with -Bernstein unions ∪ (a subset A ⊆ X is -Bernstein if A and X A meet each Borel -positive subset...
On montre que si G est un groupe abélien localment compact non diskret à base dénombrable d'ouverts, alors la famille des fermés de synthèse pour l'algèbre de Fourier A(G) est une partie coanalytique non borélienne de ℱ(G), l'ensemble des fermés de G muni de la structure borélienne d'Effros. On généralise ainsi un résultat connu dans le cas du groupe 𝕋.
Nous donnons, pour chaque niveau de complexité Γ, une caractérisation du type "test d'Hurewicz" des boréliens d'un produit de deux espaces polonais ayant toutes leurs coupes dénombrables ne pouvant pas être rendus Γ par changement des deux topologies polonaises.