Multiplicative order convergence in $f$-algebras

Abstract

A net $(x_{\alpha })$ in an $f$-algebra $E$ is said to be multiplicative order convergent to $x\in E$ if $\x_α-x\u\oc 0$ 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.

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