On regularity of topological MV-algebras

A.P Gan,F.A Deng,W Luan,Y.C Yang

doi:10.1016/j.fss.2023.108747

On regularity of topological MV-algebras

A.P Gan, F.A Deng + Show 2 more

https://doi.org/10.1016/j.fss.2023.108747

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Journal: Fuzzy Sets and Systems

Publication Date: Oct 16, 2023

Affiliation: Jiangxi Normal University, Hunan University, Beihang University

#Topological Groups #Topological Rings

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Abstract

In this paper, we characterize the unique determinacy, regularity, discreteness, triviality, connectivity of topological MV-algebras. Moreover, we investigate the ideal and the quotient topological MV-algebras. Especially, we prove that every topological MV-algebra is regular. As a consequence, we show that T0,T1,T2,T3 are equivalent for topological MV-algebras, ideal topological MV-algebras, and quotient topological MV-algebras. However, because MV-algebras are not rings or groups, the results are obtained that do not correspond to topological rings or topological groups.

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