On some properties of topological $\mathbb{MV}$-coalgebras (opens in a new tab)

Abstract

We investigate some properties of topological $\mathbb{MV}$-coalgebras, where $\mathbb{MV}$-coalgebras are coalgebras of the functor which assigns every BL-algebra to its MV-center. We show that the limit of the inverse system arising from a family of Boolean deductive systems is isomorphic to its completion, and characterize Haussdorf topological $\mathbb{MV}$-coalgebras. Moreover, we show that the category of topological $\mathbb{MV}$-coalgebras is strong-monotopological over the category of $\mathbb{MV}$-coalgebras. Finally, we establish a coalgebraic link between BL-algebras and DRl-monoids and deduce the (co)completeness of a category of coalgebras over DRl-monoids.

Keywords

• #distributed and parallel computing systems
• #advanced topics in algebra
• #topology (electrical circuits)
• #mathematics
• #physics
• #pure mathematics
• #combinatorics