  In the context of rational conformal field theories (RCFT) we look at the
fusing matrices that arise when a topological defect is attached to a conformal
boundary condition. We call such junctions open topological defects. One type
of fusing matrices arises when two open defects fuse while another arises when
an open defect passes through a boundary operator. We use the topological field
theory approach to RCFTs based on Frobenius algebra objects in modular tensor
categories to describe the general structure associated with such matrices and
how to compute them from a given Frobenius algebra object and its
representation theory. We illustrate the computational process on the rational
free boson theories. Applications to boundary renormalisation group flows are
briefly discussed.
