Metric characterizations of Banach spaces
J. E. Valentine, S. G. Wayment (1973)
Colloquium Mathematicae
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J. E. Valentine, S. G. Wayment (1973)
Colloquium Mathematicae
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Bogdan Rzepecki (1980)
Annales Polonici Mathematici
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J. Nagata (1958)
Fundamenta Mathematicae
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Tomonari Suzuki, Badriah Alamri, Misako Kikkawa (2015)
Open Mathematics
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We prove that every 3-generalized metric space is metrizable. We also show that for any ʋ with ʋ ≥ 4, not every ʋ-generalized metric space has a compatible symmetric topology.
Naidu, S.V.R., Rao, K.P.R., Srinivasa Rao, N. (2005)
International Journal of Mathematics and Mathematical Sciences
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J. E. Jayne, I. Namioka, C. A. Rogers (1990)
Collectanea Mathematica
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A Banach space which is a Cech-analytic space in its weak topology has fourteen measure-theoretic, geometric and topological properties. In a dual Banach space with its weak-star topology essentially the same properties are all equivalent one to another.
E. Andalafte, L. Blumenthal (1964)
Fundamenta Mathematicae
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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...
Kocayusufoğlu, Ịsmail, Ada, Tuba (2006)
APPS. Applied Sciences
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Sophocles K. Mercourakis, Georgios Vassiliadis (2018)
Commentationes Mathematicae Universitatis Carolinae
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