# The Banach contraction mapping principle and cohomology

Commentationes Mathematicae Universitatis Carolinae (2000)

- Volume: 41, Issue: 3, page 605-610
- ISSN: 0010-2628

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topJanoš, Ludvík. "The Banach contraction mapping principle and cohomology." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 605-610. <http://eudml.org/doc/22513>.

@article{Janoš2000,

abstract = {By a dynamical system $(X,T)$ we mean the action of the semigroup $(\mathbb \{Z\}^+,+)$ 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.},

author = {Janoš, Ludvík},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {$B$-system; $E$-system},

language = {eng},

number = {3},

pages = {605-610},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {The Banach contraction mapping principle and cohomology},

url = {http://eudml.org/doc/22513},

volume = {41},

year = {2000},

}

TY - JOUR

AU - Janoš, Ludvík

TI - The Banach contraction mapping principle and cohomology

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2000

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 41

IS - 3

SP - 605

EP - 610

AB - By a dynamical system $(X,T)$ we mean the action of the semigroup $(\mathbb {Z}^+,+)$ 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.

LA - eng

KW - $B$-system; $E$-system

UR - http://eudml.org/doc/22513

ER -

## References

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