Relatively uniform convergences in archimedean lattice ordered groups

Year, pages: 2010, 447 - 460

For an archimedean lattice ordered group $G$ let $G^d$ and $G^\wedge$ be the divisible hull or the Dedekind completion of $G$, respectively. Put $G^d\wedge=X$. Then $X$ is a vector lattice. In the present paper we deal with the relations between the relatively uniform convergence on $X$ and the relatively uniform convergence on $G$. We also consider the relations between the $o$-convergence and the relatively uniform convergence on $G$. For any nonempty class $τ$ of lattice ordered groups we introduce the notion of $τ$-radical class; we apply this notion by investigating relative uniform convergences.

Jakubík, J., Černák, Š. 2010. Relatively uniform convergences in archimedean lattice ordered groups. In Mathematica Slovaca, vol. 60, no.4, pp. 447-460. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0024-8

Jakubík, J., Černák, Š. (2010). Relatively uniform convergences in archimedean lattice ordered groups. Mathematica Slovaca, 60(4), 447-460. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0024-8