  The role of double space is essential in new interpretation of T-duality and
consequently in an attempt to construct M-theory. The case of open string is
missing in such approach because until now there have been no appropriate
formulation of open string T-duality. In the previous paper [1], we showed how
to introduce vector gauge fields $A^N_a$ and $A^D_i$ at the end-points of open
string in order to enable open string invariance under local gauge
transformations of the Kalb-Ramond field and its T-dual "restricted general
coordinate transformations". We demonstrated that gauge fields $A^N_a$ and
$A^D_i$ are T-dual to each other. In the present article we prove that all
above results can be interpreted as coordinate permutations in double space.
