We show that under some conditions on a family A ⊂ I there exists a subfamily A0 ⊂ A such that ⋃ A0 is nonmeasurable with respect to a fixed ideal I with Borel base of a fixed uncountable Polish space. Our result applies to the classical ideal of null subsets of the real line and to the ideal of first category subsets of the real line.

We consider Segal’s categorical approach to conformal field theory (CFT). Segal constructed a category whose objects are finite families of circles, and whose morphisms are Riemann surfaces with boundary compatible with the families of circles in the domain and codomain. A CFT is then defined to be a functor to the category of Hilbert spaces, preserving the appropriate structure. In particular,...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

We study the relationship between the σ-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category. As a consequence we get that the additivity of the ideal of closed measure zero sets is equal to the additivity of the ideal of meager sets.

one of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. in this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. we also devote to characterizing bijective morphisms on quantum effects leaving the witness...

The purpose of this paper is to define cohomology complexes and study deformation theory Hom-associative algebra morphisms Hom-Lie morphisms. We discuss infinitesimal deformations, e...

Abstract We investigate several questions related to the notion of recognizable morphism. The main result is a new proof Mossé’s theorem and actually generalization more general class morphisms due Berthé et al [Recognizability for sequences morphisms. Ergod. Th. & Dynam. Sys. 39 (11) (2019), 2896–2931]. prove most morphisms, including ones with erasable letters. Our derived from concerning...