Multiplicative order convergence in f-algebras

Abstract

A net (x?) in an f-algebra E is said to be multiplicative order convergent to x ? E if |x? ? x| u o?? 0 for all u ? E+. In this paper, we introduce the notions mo-convergence, moCauchy, mo-complete, mo-continuous, and mo-KB-space. Moreover, we study the basic properties of these notions.