Uniformizable and realcompact bornological universes

Tom Vroegrijk


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.


Bornology; Uniform space; Totally bounded; Realcompactness

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