Metric criteria for Banach and Euclidean spaces
L. Loveland, J. Valentine (1978)
Fundamenta Mathematicae
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Displaying similar documents to “Banach-Euclidean four-point properties”
Metric criteria for Banach and Euclidean spaces
The Menelaus Property characterizes real rotund Banach spaces
J. Valentine (1978)
Fundamenta Mathematicae
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On the singlevaluedness and differentiation of metric projections
Zajíček, L.
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Metric characterizations of Banach spaces
J. E. Valentine, S. G. Wayment (1973)
Colloquium Mathematicae
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A local metric characterization of Banach spaces
J. E. Valentine, S. G. Wayment (1981)
Colloquium Mathematicae
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Strictly convex spheres in V-spaces
Raymond Freese, Grattan Murphy (1983)
Fundamenta Mathematicae
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Metric spaces with the small ball property
Ehrhard Behrends, Vladimir M. Kadets (2001)
Studia Mathematica
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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...
On criteria of Blumenthal for inner-product spaces
Joseph Valentine (1971)
Fundamenta Mathematicae
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Metric characterizations of Banach and Euclidean spaces
E. Andalafte, L. Blumenthal (1964)
Fundamenta Mathematicae
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Example of a sequentially incomplete regular inductive limit of Banach spaces.
Kučera, Jan, McKennon, Kelly (1990)
International Journal of Mathematics and Mathematical Sciences
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Strictly convex metric spaces with round balls and fixed points
Inese Bula (2005)
Banach Center Publications
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The paper introduces a notion of strictly convex metric space and strictly convex metric space with round balls. These objects generalize the well known concept of strictly convex Banach space. We prove some fixed point theorems in strictly convex metric spaces with round balls.