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Topological Homotheties on Compact Metrizable Spaces

Published online by Cambridge University Press:  20 November 2018

Ludvik Janos
Ludvik Janos*
Affiliation:
University of Florida, Gainesville, Florida
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Notation and definitions.

Definition 1. Let (X, ρ) be a metric space and ϕ: X → X a continuous self-mapping of X. We shall call ϕ and α-contraction on (X, ρ) if and only if α ϵ [0,1) and . We shall call ϕ an α-homothety on (X, ρ) if and only if α > 0 and .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1383 - 1386
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Bing, R. H., Extending a metric, Duke Math. J. 14 (1947), 511–519.Google Scholar
2. Janos, L., Converse of the theorem on contracting mapping, Notices Amer. Math. Soc. 11 1964), 224.Google Scholar
3. Janos, L., A converse of Banach's contraction theorem, Proc. Amer. Math. Soc. 18 (1967), 287–289.Google Scholar