Dugundji's canonical covers, asymptotic and covering dimension

摘要

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 canonical covers of the complementary of X, especially 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 related questions in the literature.