Central points and measures and dense subsets of compact metric spaces
Słowa kluczowe
Chebyshev center, convex set, common fixed point, Kantorovich metric, pointed metric space, distinguishing a pointAbstrakt
For every nonempty compact convex subset $K$ of a normed linear space a (unique) point $c_K \in K$, called the generalized Chebyshev center, is distinguished. It is shown that $c_K$ is a common fixed point for the isometry group of the metric space $K$. With use of the generalized Chebyshev centers, the central measure $\mu_X$ of an arbitrary compact metric space $X$ is defined. For a large class of compact metric spaces, including the interval $[0,1]$ and all compact metric groups, another `central' measure is distinguished, which turns out to coincide with the Lebesgue measure and the Haar one for the interval and a compact metric group, respectively. An idea of distinguishing infinitely many points forming a dense subset of an arbitrary compact metric space is also presented.Pobrania
Opublikowane
2012-04-23
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1.
NIEMIEC, Piotr. Central points and measures and dense subsets of compact metric spaces. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2012, T. 40, nr 1, s. 161–180. [udostępniono 3.7.2024].
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