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Minimal ball-coverings in Banach spaces and their application

Lixin ChengQingjin ChengHuihua Shi — 2009

Studia Mathematica

By a ball-covering of a Banach space X, we mean a collection of open balls off the origin in X and whose union contains the unit sphere of X; a ball-covering is called minimal if its cardinality is smallest among all ball-coverings of X. This article, through establishing a characterization for existence of a ball-covering in Banach spaces, shows that for every n ∈ ℕ with k ≤ n there exists an n-dimensional space admitting a minimal ball-covering of n + k balls. As an application, we give a new...

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