Mathematica Bohemica

Mathematica Bohemica, first online, pp. 1-17

On some properties of topological $\mathbb{MV}$-coalgebras

Cyrille Nganteu, Maurice Kianpi, Hilaire Mbiakop

Received December 31, 2023. Published online March 3, 2025.

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

Classification MSC: 06D35, 22A26, 08C05

DOI: 10.21136/MB.2025.0183-23

PDF available at: Institute of Mathematics CAS

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Affiliations: Cyrille Nganteu (corresponding author), Maurice Kianpi, Hilaire Mbiakop, University of Yaounde 1, Faculty of Science, Department of Mathematics, Laboratory of Algebra, P.O. Box 812, Yaounde, Republic of Cameroon, e-mail: nganteu2001@yahoo.fr

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