  In this paper we discuss non-commutative and non-associative geometries that
emerge in the context of non-geometric closed string backgrounds. T-duality and
doubled field theory plays an important role in formulating the corresponding
effective action for these kind of non-geometric string backgrounds. As we will
argue, the emerging non-commutative and non-associative algebras for the closed
string (dual) coordinates and (dual) momenta can be mathematically described by
a twisted Poisson structure, in closed analogy to the phase space of a point
particle moving in the field of a magnetic monopole.
