Geodesic
Some cohomological aspects of the Banach fixed point principle
Mathematica Bohemica, Tome 136 (2011) no. 3, pp. 333-336

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Let $T\colon X\to X$ be a continuous selfmap of a compact metrizable space $X$. We prove the equivalence of the following two statements: (1) The mapping $T$ is a Banach contraction relative to some compatible metric on $X$. (2) There is a countable point separating family $\mathcal {F}\subset \mathcal {C}(X)$ of non-negative functions $f\in \mathcal {C}(X)$ such that for every $f\in \mathcal {F}$ there is $g\in \mathcal {C}(X)$ with $f=g-g\circ T$.
DOI : 10.21136/MB.2011.141653
Classification : 54H20, 54H25
Keywords: Banach contraction; cohomology; cocycle; coboundary; separating family; core 
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Janoš, Ludvík. Some cohomological aspects of the Banach fixed point principle. Mathematica Bohemica, Tome 136 (2011) no. 3, pp. 333-336. doi: 10.21136/MB.2011.141653

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