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Uniform Contractification
Published online by Cambridge University Press: 20 November 2018
Abstract
Let (X, τ) be a metrizable space and {fn: n = 1,2,…} be a commuting family of continuous mappings on X with a common fixed point ξ ∈ X such that (I) for each k = l, 2, … and (II) Then for each c ∈ (0,1), there exists a metric d on X inducing the topology τ such that , for all x, y∈X and n = l, 2, …. The above result is also generalized to Tychonoff spaces.
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- Copyright © Canadian Mathematical Society 1978