Geodesic
On the Edelstein Contractive Mapping Theorem
Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 675-678

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Let X be a metrizable topological space and f:X→X a continuous selfmapping such that for every x ∈ X the sequence of iterates {fn(x)} converges. It is proved that under these conditions the following two statements are equivalent:1. There is a metrization of X relative to which f is contractive in the sense of Edelstein.2. For any nonempty f-invariant compact subset Y of X the intersection of all iterates fn (Y) is a one-point set. The relation between this type of contractivity and the Banach contraction principle is also discussed. 
On the Edelstein Contractive Mapping Theorem. Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 675-678. doi: 10.4153/CMB-1975-118-8
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     title = {On the {Edelstein} {Contractive} {Mapping} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {675--678},
     year = {1975},
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     number = {5},
     doi = {10.4153/CMB-1975-118-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-118-8/}
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