Compactness in MV-topologies: Tychonoff theorem and Stone-Čech compactification (Q2288330)

The counterpart of Tychonoff's theorem is proved for MV-topological spaces. As a consequence, it is shown that (i) products exist in the category of Stone MV-spaces, and (ii) coproducts exist in the category of limit cut complete MV-algebras. Further, these statements are shown to be ZFC-equivalent to Tychonoff's theorem. An extension of the Stone-Čech compactification functor is established for MV-topological spaces.