Multiplicative order convergence in $f$-algebras

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,

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Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

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