Journal of Convex Analysis 20 (2013), No. 1, 285--299
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 Bourbaki-bounded sets.
Keywords: Metric bounded sets, bornological universe, totally-bounded sets, Bourbaki-bounded sets, uniform equivalent metrics.
MSC: 54E35, 54E45; 46A17
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