Given a nowheredense closed subset X of a metrizable compact space X, we characterize the dimension of X in terms of the multiplicity of the canonicals covers of the complementary of X, specially in some particular cases, like when X is the Hilbert cube or the finite dimensional cube and X, a Z-set of X. In this process, we solve some questions in the literature. arXiv:1306.5572v1 [math.GN]