
Journal of Convex Analysis 24 (2017), No. 4, 10851098 Copyright Heldermann Verlag 2017 Cauchy Metrizability of Bornological Universes Manisha Aggarwal Dept. of Mathematics, Indian Institute of Technology, New Delhi 110016, India manishaaggarwal.iitd@gmail.com Subiman Kundu Dept. of Mathematics, Indian Institute of Technology, New Delhi 110016, India skundu@maths.iitd.ac.in We call a bornology on a metric space (X, d) dCauchy metrizable if there exists a metric ρ on X, Cauchy equivalent to d, such that the family of ρbounded subsets coincides with the bornology. Recall that two metrics on a set are said to be Cauchy equivalent if the collections of Cauchy sequences with respect to both the metrics are same. In this paper we give necessary and sufficient conditions for a bornology on a metric space (X, d) to be dCauchy metrizable. We solve this problem for two different approaches, one given by S.T. Hu [Boundedness in a topological space, J. Math. Pures Appl. 28 (1949) 287320; Introduction to General Topology, HoldenDay, San Francisco (1966)] and the other given by G. Beer [On metric boundedness structures, SetValued Anal. 7 (1999) 195208]. Furthermore, we investigate the same for some most common bornologies. Keywords: Cauchy continuous function, Cauchy equivalent metrics, bornology, bounded set, totally bounded, metric mode of convergence to infinity. MSC: 54E35; 46A17 [ Fulltextpdf (156 KB)] for subscribers only. 