Metric characterizations of Banach spaces
J. E. Valentine, S. G. Wayment (1973)
Colloquium Mathematicae
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Displaying similar documents to “Metric characterizations of Banach and Euclidean spaces”
Metric characterizations of Banach spaces
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Metric spaces with the small ball property
Ehrhard Behrends, Vladimir M. Kadets (2001)
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A metric space (M,d) is said to have the small ball property (sbp) if for every ε₀ > 0 it is possible to write M as the union of a sequence (B(xₙ,rₙ)) of closed balls such that the rₙ are smaller than ε₀ and lim rₙ = 0. We study permanence properties and examples of sbp. The main results of this paper are the following: 1. Bounded convex closed sets in Banach spaces have sbp only if they are compact. 2. Precisely the finite-dimensional Banach spaces have sbp. (More generally: a complete...
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