Displaying similar documents to “Metric projections of closed subspaces of c₀ onto subspaces of finite codimension”

Strongly proximinal subspaces of finite codimension in C(K)

S. Dutta, Darapaneni Narayana (2007)

Colloquium Mathematicae

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We characterize strongly proximinal subspaces of finite codimension in C(K) spaces. We give two applications of our results. First, we show that the metric projection on a strongly proximinal subspace of finite codimension in C(K) is Hausdorff metric continuous. Second, strong proximinality is a transitive relation for finite-codimensional subspaces of C(K).

On the Lifshits Constant for Hyperspaces

K. Leśniak (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

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The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.