Weak relatively uniform convergences on MV-algebras

Year, pages: 2013, 13 - 32

Weak relatively uniform convergences ($wru$-convergences, for short) in lattice ordered groups have been investigated in previous authors' papers. In the present article, the analogous notion for MV-algebras is studied. The system $s(A)$ of all $wru$-convergences on an MV-algebra $A$ is considered; this system is partially ordered in a natural way. Assuming that the MV-algebra $A$ is divisible, we prove that $s(A)$ is a Brouwerian lattice and that there exists an isomorphism of $s(A)$ into the system $s(G)$ of all $wru$-convergences on the lattice ordered group $G$ corresponding to the MV-algebra $A$. Under the assumption that the MV-algebra $A$ is archimedean and divisible, we investigate atoms and dual atoms in the system $s(A)$.

Černák, Š., Jakubík, J. 2013. Weak relatively uniform convergences on MV-algebras. In Mathematica Slovaca, vol. 63, no.1, pp. 13-32. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0078-x

Černák, Š., Jakubík, J. (2013). Weak relatively uniform convergences on MV-algebras. Mathematica Slovaca, 63(1), 13-32. 0139-9918. DOI: https://doi.org/10.2478/s12175-012-0078-x