2 results
Uniform Contractification
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- Journal:
- Canadian Mathematical Bulletin / Volume 21 / Issue 1 / 01 March 1978
- Published online by Cambridge University Press:
- 20 November 2018, pp. 93-97
- Print publication:
- 01 March 1978
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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.
and (II) 
Then for each c ∈ (0,1), there exists a metric 
, for all x, y∈X and n = l, 2, …. The above result is also generalized to Tychonoff spaces.On the Representation of Mappings of Tychonov Spaces as Restrictions of Linear Transformations
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- Journal:
- Canadian Mathematical Bulletin / Volume 19 / Issue 1 / 01 March 1976
- Published online by Cambridge University Press:
- 20 November 2018, pp. 53-57
- Print publication:
- 01 March 1976
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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.
the collection of all families of pseudometrics on 
for some 