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An application of combinatorial techniques to a topological problem
Published online by Cambridge University Press: 17 April 2009
Abstract
The following statement is proved: Let X be a set having at most continuously many elements and f: X → X a mapping such that each iteration fn (n = 1, 2, …) has a unique fixed point. Then for every number c ∈ (0, 1) there exists a metric p on X such that the metric space (X, p) is separable and the mapping f is a.contraction with the Lipschitz constant c.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 9 , Issue 3 , December 1973 , pp. 439 - 443
- Copyright
- Copyright © Australian Mathematical Society 1973
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