  It is known that for any full rational conformal field theory, the
correlation functions that are obtained by the TFT construction satisfy all
locality, modular invariance and factorization conditions, and that there is a
small set of fundamental correlators to which all others are related via
factorization - provided that the world sheets considered do not contain any
non-trivial defect lines. In this paper we generalize both results to oriented
world sheets with an arbitrary network of topological defect lines.
