  In this manuscript we study the cosmological constant of a
$(p+1)$-dimensional world, which lives in the higher dimensional bulk space. We
assume the extra dimensions are compact on tori. We consider two cases:
positive and negative bulk cosmological constant. It is pointed out that the
tiny cosmological constant of our world can be obtained by the dynamics of a
scalar field and adjusting the parameters of the model. The cosmological
constant of the dual world also will be discussed. We obtain the Dirac
quantization of these cosmological constants.
