Multiplicative order convergence in f-algebras

Abstract

A net (xα) in an f-algebra E is said to be multiplicative order convergent to x ∈ E if|xα − 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 basicproperties of these notions.