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This paper focus on establishing in a unified way metric structures on some MTL-algebras. Let M be one of the R0-algebra, MV -algebra, product algebra and G-algebra, ΩM be the set of all homomorphisms from M into the real unit interval [0; 1], and μ be a probability measure on ΩM. It is proved that these MTL-algebras (R0-algebra, MV -algebra, product algebra and G-algebra) are standardly separable,...
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