Ludvík Janoš, PO Box 1563, Claremont, CA 91711, USA
Abstract: Let $T X\to X$ 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 $f=g-g\circ T$.
Keywords: Banach contraction, cohomology, cocycle, coboundary, separating family, core
Classification (MSC 2010): 54H25, 54H20
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