Some cohomological aspects of the Banach fixed point principle
Ludvík Janoš (2011)
Mathematica Bohemica
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Let be a continuous selfmap of a compact metrizable space . We prove the equivalence of the following two statements: (1) The mapping is a Banach contraction relative to some compatible metric on . (2) There is a countable point separating family of non-negative functions such that for every there is with .