A simple characterization of the existence of upper semicontinuous order-preserving functions

Gianni Bosi () and Laura Franzoi
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Gianni Bosi: University of Trieste
Laura Franzoi: University of Trieste

Economic Theory Bulletin, 2023, vol. 11, issue 2, No 4, 203-210

Abstract: Abstract We introduce an upper semicontinuity condition concerning a not necessarily total preorder on a topological space, namely strong upper semicontinuity, and in this way we extend to the nontotal case the famous Rader’s theorem, which guarantees the existence of an upper semicontinuous order-preserving function for an upper semicontinuous total preorder on a second countable topological space. We show that Rader’s theorem is not generalizable if we adopt weaker upper semicontinuity conditions already introduced in the literature. We characterize the existence of an upper semicontinuous order-preserving function for all strongly upper semicontinuous preorders on a metrizable topological space.

Keywords: Order-preserving function; Upper semicontinuous function; Strongly upper semicontinuous preorder; C60; D01 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s40505-023-00251-9

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