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  • Rule: asEquivalentb3sb3sifpdbprdf-labelfacetshttp://dbpedia.org/resource/inference/rules/dbpedia#http://dbpedia.org/resource/inference/rules/opencyc#http://dbpedia.org/resource/inference/rules/umbel#http://dbpedia.org/resource/inference/rules/yago#http://dbpedia.org/schema/property_rules#http://localhost:8890/dataspacehttp://www.ontologyportal.org/inference/rules/SUMO#http://www.ontologyportal.org/inference/rules/WordNet#http://www.w3.org/2002/07/owl#ldpoplwebskos-transvirtrdf-labelvirtrdf-urlNone
    
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In functional analysis, a branch of mathematics, the Ryll-Nardzewski fixed-point theorem states that if is a normed vector space and is a nonempty convex subset of that is compact under the weak topology, then every group (or equivalently: every semigroup) of affine isometries of has at least one fixed point. (Here, a fixed point of a set of maps is a point that is fixed by each map in the set.) This theorem was announced by Czesław Ryll-Nardzewski. Later Namioka and Asplund gave a proof based on a different approach. Ryll-Nardzewski himself gave a complete proof in the original spirit.