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An EMV-algebra resembles an MV-algebra in which a top element is not guaranteed. For $\unicode[STIX]{x1D70E}$ -complete $EMV$ -algebras, we prove an analogue of the Loomis–Sikorski theorem showing that every $\unicode[STIX]{x1D70E}$ -complete $EMV$ -algebra is a $\unicode[STIX]{x1D70E}$ -homomorphic image of an $EMV$ -tribe of fuzzy sets where all algebraic operations are defined by points. To prove it, some topological properties of the state-morphism space and the space of maximal ideals are established.


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The first author is grateful for support from grants APVV-16-0073, VEGA no. 2/0069/16 SAV and GAČR 15-15286S.



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