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On the Representation of Mappings of Tychonov Spaces as Restrictions of Linear Transformations
Published online by Cambridge University Press: 20 November 2018
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Let (X, τ) be a Tychonov space and 
the collection of all families of pseudometrics on X generating the topology τ on X. Let f:X→X and c>0. Then f is said to be a topological c-homothety if there exists some B in such that d(f(x), f(y))=cd(x, y) for all d ∈ B and all x, y in X (see [4]). We say that f can be linearized in L as a c-homothety if there exists a linear topological space L, and a topological embedding i:X→L such that i(f(x))=ci(x) for all x in X (see [4]).f is said to be squeezing if 
for some a in X.
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- Research Article
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- Copyright © Canadian Mathematical Society 1976
References
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Janos, L., Topological homothetics on compact Hausdorff spaces, Proc. Amer. Math. Soc. Vol.
21 (1969) 562–568.Google Scholar
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