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Regular representations of semisimple MV-algebras by continuous real functions. (English) Zbl 0987.06010
With any topological space \(M\) one can associate the MV-algebra \(A_1(M)\) corresponding to the \(\ell \)-group of all continuous bounded real functions on \(M\). If \(A\) is an MV-algebra and \(M\) a topological space, then an injective morphism \(\varphi \:A\to A_1(M)\) will be called a representation of \(A\) by continuous real functions. A representation is regular if it preserves the suprema (and the infima).
It is proved here that for any semisimple MV-algebra \(A\) there exists an extremal compact Hausdorff space \(M\) and a regular representation \(\varphi:A \to A_1(M)\).

MSC:
06D35 MV-algebras
54C40 Algebraic properties of function spaces in general topology
54C30 Real-valued functions in general topology
54D30 Compactness
06F15 Ordered groups
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