Some results on topological MV-algebras

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 MValgebras 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(A) of set-theoretic filters on proto-MV-algebra A. These operations make (omega(A), +,' , up arrow 0) a proto-MV-algebra. Especially, we establish a relationship between the category PMV and the category TPMV. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data