- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 3
- Multiplicative order convergence in $f$-algebras
Multiplicative order convergence in $f$-algebras
Authors : Abdullah Aydin
Pages : 998-1005
Doi:10.15672/hujms.512073
View : 7 | Download : 3
Publication Date : 2020-06-02
Article Type : Research
Abstract :A net $(x_\alpha)$ in an $f$-algebra $E$ is said to be multiplicative order convergent to $x\in E$ if $\left|x_\alpha-x\right|u\oc 0$ for all $u\in E_+$. In this paper, we introduce the notions $mo$-convergence, $mo$-Cauchy, $mo$-complete, $mo$-continuous, and $mo$-KB-space. Moreover, we study the basic properties of these notions.Keywords : $mo$-convergence, $f$-algebra, $mo$-KB-space, vector lattice