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Linearization of a Contractive Homeomorphism

Published online by Cambridge University Press:  20 November 2018

Ludvik Janos
Ludvik Janos*
Affiliation:
University of Florida, Gainesville, Florida
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Let X be a topological space and ϕ: X ⟶ X a continuous self-mapping of X. We say that ϕ is linearized in L by Φ if there exists a topological embedding μ: X ⟶ L of the space X into the linear topological vector space L such that for all x ϵ X, μ (ϕ (x)) = Φ (μ (x)), where ϕ is a continuous linear operator on L.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1387 - 1390
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Janos, Ludvik, One-to-one contractive mappings on compact spaces, Notices Amer. Math. Soc. 14 (1967), 133.Google Scholar