  We reconsider some older constructions of T-duality, based on automorphisms
of the worldsheet operator algebra, in a modern context. It has been long known
that at special points in the moduli space of torus compactifications, the
target space gauge symmetry may be enhanced. Away from such points the symmetry
is broken and T-duality may be understood as a residual discrete gauge symmetry
that survives this breaking. Drawing on work on connections over the space of
string backgrounds, we discuss how to generalise this framework for T-duality
to geometric and non-geometric backgrounds that are not full solutions of
string theory, but may play an important role in exact backgrounds. Along the
way we find an interesting algebraic structure and discuss its relationship
with doubled geometry. We comment on non-isometric T-duality in this context.
