  Compact Hausdorff topological MV-algebras and Stone MV-algebras are
completely characterized. We obtain that compact Hausdorff topological
MV-algebras are product (both topological and algebraic) of copies $[0,1]$ with
standard topology and finite Lukasiewicz chains with discrete topology. Going
one step further we also prove that Stone MV-algebras are product (both
topological and algebraic) of finite Lukasiewicz chains with discrete topology.
We also prove that an MV-algebra is strongly complete (isomorphic to its
profinite completion) if and only if it is profinite and its maximal ideals of
finite ranks are principal.
