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Keywords:
BL-algebra; topological $\mathbb {MV}$-coalgebra; topological category
BL-algebra; topological $\mathbb {MV}$-coalgebra; topological category
Summary:
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.
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