  In the paper [1] we showed that in double space, where all initial
coordinates $x^\mu$ are doubled $x^\mu \to y_\mu$, the T-duality
transformations can be performed by exchanging places of some coordinates $x^a$
and corresponding dual coordinates $y_a$. Here we generalize this result to the
case of weakly curved background where in addition to the extended coordinate
we will also transform extended argument of background fields with the same
operator $\hat {\cal T}^a$. So, in the weakly curved background T-duality leads
to the physically equivalent theory and complete set of T-duality
transformations form the same group as in the flat background. Therefore, the
double space represent all T-dual theories in unified manner.
