  We introduce the $2D$ dimensional double space with the coordinates $Z^M=
(x^\mu, y_\mu)$ which components are the coordinates of initial space $x^\mu$
and its T-dual $y_\mu$. We shall show that in this extended space the T-duality
transformations can be realized simply by exchanging places of some coordinates
$x^a$, along which we want to perform T-duality and the corresponding dual
coordinates $y_a$. In such approach it is evident that T-duality leads to the
physically equivalent theory and that complete set of T-duality transformations
form subgroup of the $2D$ permutation group. So, in the double space we are
able to represent the backgrounds of all T-dual theories in unified manner.
