Weak relatively uniform convergences on abelian lattice ordered groups

Rok, strany: 2011, 687 - 704

The notion of relatively uniform convergence has been applied in the theory of vector lattices and in the theory of archimedean lattice ordered groups. Let $G$ be an abelian lattice ordered group. In the present paper we introduce the notion of weak relatively uniform convergence (wru-convergence, for short) on $G$ generated by a system $M$ of regulators. If $G$ is archimedean and $M=G⁺$, then this type of convergence coincides with the relative uniform convergence on $G$. The relation of wru-convergence to the $o$-convergence is examined. If $G$ has the diagonal property, then the system of all convex $\ell$-subgroups of $G$ closed with respect to wru-limits is a complete Brouwerian lattice. The Cauchy completeness with respect to wru-convergence is dealt with. Further, there is established that the system of all wru-convergences on an abelian divisible lattice ordered group $G$ is a complete Brouwerian lattice.

ISO 690:

Černák, Š., Jakubík, J. 2011. Weak relatively uniform convergences on abelian lattice ordered groups. In Mathematica Slovaca, vol. 61, no.5, pp. 687-704. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0039-9

APA:

Černák, Š., Jakubík, J. (2011). Weak relatively uniform convergences on abelian lattice ordered groups. Mathematica Slovaca, 61(5), 687-704. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0039-9