Some results on topological MV-algebras

Abstract

First of all, in this paper, we give an equivalent characterization for a finite topological MV-algebra satisfying the open condition. In addition, we investigate the topological isomorphism theorems and other related results of topological MV-algebras with the open condition. Then we study the initial topology of topological MV-algebras. Moreover, we introduce the concept of proto-MV-algebras and two operations ∔ and ′ on the family $\omega \left(A\right)$ of set-theoretic filters on proto-MV-algebra A. These operations make $\left(\omega \right(A),\dotplus ,\prime ,\uparrow 0)$ a proto-MV-algebra. Especially, we establish a relationship between the category $\mathrm{PMV}$ and the category $\mathrm{TPMV}$.