In double field theory, the T-duality transformation of exchanging momentum and winding modes of closed strings on toroidal backgrounds translates to a generalized coordinate transformation on a doubled spacetime, where one set of its coordinates is dual to momentum modes and the second set of coordinates is interpreted as dual to winding modes of the closed string. Whether the second set of coordinates has physical meaning depends on how the level-matching condition of closed strings is implemented in the theory: either through the weak constraint or the strong constraint.