
Journal of Convex Analysis 20 (2013), No. 1, 285299 Copyright Heldermann Verlag 2013 Uniformly Metrizable Bornologies Isabel Garrido Dep. de Geometría y Topología, Universidad Complutense de Madrid, 28040 Madrid, Spain maigarri@mat.ucm.es Ana S. Merono Dep. de Geometría y Topología, Universidad Complutense de Madrid, 28040 Madrid, Spain anamerogno@gmail.com 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 Bourbakibounded sets. Keywords: Metric bounded sets, bornological universe, totallybounded sets, Bourbakibounded sets, uniform equivalent metrics. MSC: 54E35, 54E45; 46A17 [ Fulltextpdf (158 KB)] for subscribers only. 