  We present a new type of gravitational mass defect in which an infinite
amount of matter may be bounded in a zero ADM mass. This interpolates between
effects typical of closed worlds and T-spheres. We consider the Tolman model of
dust distribution and show that this phenomenon reveals itself for a solution
that has no origin on one side but is closed on the other side. The second
class of examples corresponds to smooth gluing T-spheres to the portion of the
Friedmann-Robertson-Walker solution. The procedure is generalized to
combinations of smoothly connected T-spheres, FRW and Schwarzschild metrics. In
particular, in this approach a finite T-sphere is obtained that looks for
observers in two R-regions as the Schwarzschild metric with two different
masses one of which may vanish.
