  In this paper, we discuss some questions about compactness in MV-topological
spaces. More precisely, we first present a Tychonoff theorem for such a class
of fuzzy topological spaces and some consequence of this result, among which,
for example, the existence of products in the category of Stone MV-spaces and,
consequently, of coproducts in the one of limit cut complete MV-algebras. Then
we show that our Tychonoff theorem is equivalent, in ZF, to the Axiom of
Choice, classical Tychonoff theorem, and Lowen's analogous result for
lattice-valued fuzzy topology. Last, we show an extension of the Stone-Cech
compactification functor to the category of MV-topological spaces, and we
discuss its relationship with previous works on compactification for fuzzy
topological spaces.
