Regular representations of semisimple MV-algebras by continuous real functions (Q2777534)

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). NEWLINENEWLINENEWLINEIt is proved here that for any semisimple MV-algebra \(A\) there exists an extremal compact Hausdorff space \(M\) and a regular representation \(\varphi:A \to A_1(M)\).