Geodesic
Uniformly Metrizable Bornologies
Journal of convex analysis, Tome 20 (2013) no. 1, pp. 285-299 Cet article a éte moissonné depuis la source Heldermann Verlag

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This paper is devoted to study the following question: given a bornology B on a metric space (X,d), when is there a metric d' on X, uniformly equivalent to d, for which the bornology of d'-bounded sets coincides with B ? If that happens, we will say that B is uniformly metrizable. We characterize these kinds of bornologies on X, and we obtain necessary and sufficient conditions in order to some of the most common bornologies enjoy this property. More precisely, we will consider the compact bornology, the totally bounded bornology and the bornology of the Bourbaki-bounded sets.
Classification : 54E35, 54E45, 46A17
Mots-clés : Metric bounded sets, bornological universe, totally-bounded sets, Bourbaki-bounded sets, uniform equivalent metrics 
@article{JCA_2013_20_1_JCA_2013_20_1_a17,
     author = {I. Garrido and A. S. Merono},
     title = {Uniformly {Metrizable} {Bornologies}},
     journal = {Journal of convex analysis},
     pages = {285--299},
     year = {2013},
     volume = {20},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a17/}
}
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I. Garrido; A. S. Merono. Uniformly Metrizable Bornologies. Journal of convex analysis, Tome 20 (2013) no. 1, pp. 285-299. http://geodesic.mathdoc.fr/item/JCA_2013_20_1_JCA_2013_20_1_a17/