Relatively uniform convergences in archimedean lattice ordered groups

Mathematica Slovaca

Ján Jakubík¹  Štefan Černák¹ 

关键词: lattice ordered group;    vector lattice;    relatively uniform convergence;    o-convergence;   

DOI  :  10.2478/s12175-010-0024-8

学科分类：数学（综合）

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

【 摘 要 】

For an archimedean lattice ordered group G let G d and G∧ be the divisible hull or the Dedekind completion of G, respectively. Put G d∧ = 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.

【 授权许可】

Unknown