Central points and measures and dense subsets of compact metric spaces
Keywords
Chebyshev center, convex set, common fixed point, Kantorovich metric, pointed metric space, distinguishing a pointAbstract
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.Downloads
Published
2012-04-23
How to Cite
1.
NIEMIEC, Piotr. Central points and measures and dense subsets of compact metric spaces. Topological Methods in Nonlinear Analysis. Online. 23 April 2012. Vol. 40, no. 1, pp. 161 - 180. [Accessed 24 April 2024].
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