In this thesis we discuss the concepts of inverse spectra, their limits and morphisms, and inspect the behavior of certain topological properties under the operation of the limit of an inverse spectrum. We introduce the most used notions of dimension of topological spaces: the small and large inductive dimension, and the covering dimension. We discuss the properties of said dimensions. We prove the coincidence theorem for dimensions on the class of separable metric spaces. We then prove two theorems that connect these two theories; one of them states that a topological space is compact and Hausdorff with dimension less than or equal to n if and only if it is a limit of an inverse spectrum of metrisable compacta of dimension less than or equal to n; the other theorem states an analogous equivalence for metrisable compacta and limits of inverse sequences of polyhedra.
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