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Uniform Contractification

Published online by Cambridge University Press:  20 November 2018

Kok-Keong Tan*
Affiliation:
Mathematics Department, Dalhousie University Halifax, Nova Scotia Canada B3H 4H8
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1978

References

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