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Title: The Banach contraction mapping principle and cohomology (English)
Author: Janoš, Ludvík
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 41
Issue: 3
Year: 2000
Pages: 605-610
Category: math
Summary: By a dynamical system $(X,T)$ we mean the action of the semigroup $(\Bbb Z^+,+)$ on a metrizable topological space $X$ induced by a continuous selfmap $T:X\rightarrow X$. Let $M(X)$ denote the set of all compatible metrics on the space $X$. Our main objective is to show that a selfmap $T$ of a compact space $X$ is a Banach contraction relative to some $d_1\in M(X)$ if and only if there exists some $d_2\in M(X)$ which, regarded as a $1$-cocycle of the system $(X,T)\times (X,T)$, is a coboundary. (English)
Keyword: $B$-system
Keyword: $E$-system
MSC: 37B25
MSC: 37B99
MSC: 47H10
MSC: 54H15
MSC: 54H20
MSC: 54H25
idZBL: Zbl 1087.37502
idMR: MR1795089
Date available: 2009-01-08T19:05:33Z
Last updated: 2012-04-30
Stable URL:
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