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The Structure of Extended Real-valued Metric Spaces

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Abstract

An extended metric on a set X is a distance function that satisfies the usual properties of a metric except that it can assume values of infinity, in addition to nonnegative real values. Given a metrizable space we exhibit a universal space for all extended metric spaces compatible with the topology. Defining a set in an extended metric space to be bounded if it is contained in a finite union of open balls, we characterize those bornologies on X that can be realized as bornologies of metrically bounded sets. We also consider a second possible definition of bounded set in this setting.

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Authors and Affiliations

  1. Department of Mathematics, California State University Los Angeles, 5151 State University Drive, Los Angeles, CA, 90032, USA

    Gerald Beer

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  1. Gerald Beer
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Correspondence to Gerald Beer.

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Dedicated to Petar Kenderov on his 70th birthday.

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Beer, G. The Structure of Extended Real-valued Metric Spaces. Set-Valued Var. Anal 21, 591–602 (2013). https://doi.org/10.1007/s11228-013-0255-2

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  • DOI: https://doi.org/10.1007/s11228-013-0255-2

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