{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T12:00:14Z","timestamp":1768564814953,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T00:00:00Z","timestamp":1768003200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We characterize the upper semicontinuous representability of a semiorder \u227a as an interval order (namely, by a pair (u,v) of upper semicontinuous real-valued functions) on a topological space with a countable basis of open sets, where one of the representing functions is a one-way utility for the characteristic weak order \u227a0 associated with the semiorder. Such a description generalizes the upper semicontinuous threshold representation. To this end, we introduce a suitable upper semicontinuity condition concerning a semiorder, namely strict upper semicontinuity. We further characterize the mere existence of an upper semicontinuous one-way utility for this characteristic weak order, with a view to the identification of maximal elements on compact metric spaces.<\/jats:p>","DOI":"10.3390\/axioms15010053","type":"journal-article","created":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T08:20:37Z","timestamp":1768206037000},"page":"53","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Upper Semicontinuous Representations of Semiorders as Interval Orders"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3799-4630","authenticated-orcid":false,"given":"Gianni","family":"Bosi","sequence":"first","affiliation":[{"name":"Department of Economics, Business, Mathematics and Statistics, University of Trieste, Via Valerio 4\/1, 34127 Trieste, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3500-6843","authenticated-orcid":false,"given":"Gabriele","family":"Sbaiz","sequence":"additional","affiliation":[{"name":"Department of Economics, Business, Mathematics and Statistics, University of Trieste, Via Valerio 4\/1, 34127 Trieste, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9311-6325","authenticated-orcid":false,"given":"Magal\u00ec","family":"Zuanon","sequence":"additional","affiliation":[{"name":"Department of Economics and Management, University of Brescia, Contrada Santa Chiara 50, 25122 Brescia, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"178","DOI":"10.2307\/1905751","article-title":"Semiorders and a theory of utility discrimination","volume":"24","author":"Luce","year":"1956","journal-title":"Econometrica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1086\/288173","article-title":"Extensive measurement in semiorders","volume":"34","author":"Krantz","year":"1967","journal-title":"Philos. 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