Generalized topologies for statistical metric spaces
E. Thorp (1962)
Fundamenta Mathematicae
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E. Thorp (1962)
Fundamenta Mathematicae
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R. Stevens (1967)
Fundamenta Mathematicae
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Naidu, S.V.R., Rao, K.P.R., Srinivasa Rao, N. (2005)
International Journal of Mathematics and Mathematical Sciences
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J. Nagata (1958)
Fundamenta Mathematicae
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J. de Groot (1958)
Colloquium 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.
Holá, L’. (1997)
Serdica Mathematical Journal
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Let (X, d) be a metric space and CL(X) the family of all nonempty closed subsets of X. We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric d forces X to be a compact space. In the literature only a more involved and indirect proof using the proximal topology is known. Here we do not need this intermediate step. Moreover we prove that (X, d) is boundedly compact if and only if the bounded Vietoris and Wijsman topologies...
Claudi Alsina, Enric Trillas (1977)
Stochastica
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In the present note we study the effective construction of a natural generalized metric structure (on a set), obtaining as particular case the result of Menger. In the case of groups, we analyze its topology and its structure of natural proximity space (in the sense of Efremovic).
Calvin F. K. Jung (1968)
Colloquium Mathematicae
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