Displaying similar documents to “Homeomorphisms of inverse limits of metric spaces”

Finite-to-one maps and dimension

Jerzy Krzempek (2004)

Fundamenta Mathematicae

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It is shown that for every at most k-to-one closed continuous map f from a non-empty n-dimensional metric space X, there exists a closed continuous map g from a zero-dimensional metric space onto X such that the composition f∘g is an at most (n+k)-to-one map. This implies that f is a composition of n+k-1 simple ( = at most two-to-one) closed continuous maps. Stronger conclusions are obtained for maps from Anderson-Choquet spaces and ones that satisfy W. Hurewicz's condition (α). The...

Approximate inverse systems of uniform spaces and an application of inverse systems

Michael G. Charalambous (1991)

Commentationes Mathematicae Universitatis Carolinae

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The fundamental properties of approximate inverse systems of uniform spaces are established. The limit space of an approximate inverse sequence of complete metric spaces is the limit of an inverse sequence of some of these spaces. This has an application to the dimension of the limit space of an approximate inverse system. A topologically complete space with dim ≤ n is the limit of an approximate inverse system of metric polyhedra of dim ≤ n . A completely metrizable separable space with dim ≤ n is the...