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We introduce and study the concept of characteristic for metrics. It turns out that metrizable spaces endowed with an L*-operator which admit a metric of characteristic zero play an important role in the theory of fixed points. We prove the existence of such spaces among infinite-dimensional linear topological spaces.
A notion of L^*-spaces is investigated as a generalization of convex subspaces. This gives some topological extensions for celebrated theorems due to Maynard Smith, Brouwer and Nash.
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