Weak relatively uniform convergences on abelian lattice ordered groups

Mathematica Slovaca

Ján Jakubík¹  Štefan Černák¹ 

关键词: lattice ordered group;    relatively uniform convergence;    weak relatively uniform convergence;    regulator;    o-convergence;    Cauchy completion;    Brouwerian lattice.;   

DOI  :  10.2478/s12175-011-0039-9

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

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 â„“-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.

【 授权许可】

Unknown