Topologies for the Continuous Representability of All Continuous Total Preorders

Gianni Bosi () and Magalì Zuanon ()
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Gianni Bosi: Università di Trieste
Magalì Zuanon: Università degli Studi di Brescia

Journal of Optimization Theory and Applications, 2021, vol. 188, issue 2, No 6, 420-431

Abstract: Abstract In this paper, we present a new simple axiomatization of useful topologies, i.e., topologies on an arbitrary set, with respect to which every continuous total preorder admits a continuous utility representation. In particular, we show that, for completely regular spaces, a topology is useful, if and only if it is separable, and every isolated chain of open and closed sets is countable. As a specific application to optimization theory, we characterize the continuous representability of all continuous total preorders, which admit both a maximal and a minimal element.

Keywords: Useful topology; Complete separable system; Weak topology; Completely regular space; 54A05; 91B02; 91B16 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-020-01790-y

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