  We present a manifestly T-dual formulation of curved spaces such as an AdS
space. For group manifolds related by the orthogonal vielbein fields the three
form H=dB in the doubled space is universal at least locally. We construct an
affine nondegenerate doubled bosonic AdS algebra to define the AdS space with
the Ramond-Ramond flux. The non-zero commutator of the left and right momenta
leads to that the left momentum is in an AdS space while the right momentum is
in a dS space. Dimensional reduction constraints and the physical AdS algebra
are shown to preserve all the doubled coordinates.
