I wonder if there is a result on the unique factorization of manifolds.
Call a topological manifold to be indecomposable if it is not homeomorphic to a product of manifolds of positive dimension. Is every manifold a unique (up to order) product of indecomposable ones?
I couldn't find any statements on this simple question. Are there any results on this? Any result in different categories (smooth, complex, Riemannian or whatever) or with extra conditions is fine.
 The answer seems to be No in most cases. Can we impose strong conditions so that the answer is positive?