  We clarify the role of the dual coordinates as described from the
perspectives of the Buscher T-duality rules and Double Field Theory. We show
that the T-duality angular dual coordinates cannot be identified with Double
Field Theory dual coordinates in any of the proposals that have been made in
the literature for patching the doubled spaces. In particular, we show with
explicit examples that the T-duality angular dual coordinates can have
non-trivial transition functions over a spacetime and that their identification
with the Double Field Theory dual coordinates is in conflict with proposals in
which the latter remain inert under the patching of the B-field. We then
demonstrate that the Double Field Theory coordinates can be identified with
some C-space coordinates and that the T-dual spaces of a spacetime are
subspaces of the gerbe in C-space. The construction provides a description of
both the local $O(d,d)$ symmetry and the T-dual spaces of spacetime.
