Uniformizable and realcompact bornological universes

Tom Vroegrijk

Belgium

University of Antwerp

University of Antwerp, Middelheimlaan 1, 2000 Antwerpen, Belgium.

Submitted: 2013-09-30

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Accepted: 2013-09-30

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DOI: https://doi.org/10.4995/agt.2009.1740
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Keywords:

Bornology, Uniform space, Totally bounded, Realcompactness

Supporting agencies:

This research was not funded

Abstract:

Bornological universes were introduced some time ago by Hu and obtained renewed interest in recent articles on convergence in hyperspaces and function spaces and optimization theory. One o fHu's results gives us a necessary and sufficient condition for which a bornological universe is metrizable. In this article we will extend thi sresult and give a characterization of uniformizable bornological universes. Furthermore, a construction on bornological universes that the author used to find the bornological dual of function spaces endowed with the bounded-open topology will be used to define realcompactness for bornological universes. We will also give various characterizations of this new concept.
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