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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.