{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T04:07:21Z","timestamp":1768882041952,"version":"3.49.0"},"reference-count":32,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2012,2,29]],"date-time":"2012-02-29T00:00:00Z","timestamp":1330473600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Is there any Cartesian-closed category of continuous domains that would be closed under Jones and Plotkin's probabilistic powerdomain construction? This is a major open problem in the area of denotational semantics of probabilistic higher-order languages. We relax the question, and look for quasi-continuous dcpos instead. We introduce a natural class of such quasi-continuous dcpos, the omega-QRB-domains. We show that they form a category omega-QRB with pleasing properties: omega-QRB is closed under the probabilistic powerdomain functor, under finite products, under taking bilimits of expanding sequences, under retracts, and even under so-called quasi-retracts. But... omega-QRB is not Cartesian closed. We conclude by showing that the QRB domains are just one half of an FS-domain, merely lacking control.<\/jats:p>","DOI":"10.2168\/lmcs-8(1:14)2012","type":"journal-article","created":{"date-parts":[[2012,9,6]],"date-time":"2012-09-06T10:03:11Z","timestamp":1346925791000},"source":"Crossref","is-referenced-by-count":8,"title":["QRB-Domains and the Probabilistic Powerdomain"],"prefix":"10.46298","volume":"Volume 8, Issue 1","author":[{"given":"Jean","family":"Goubault-Larrecq","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2012,2,29]]},"reference":[{"key":"10.2168\/LMCS-8(1:14)2012_AJ:domains","doi-asserted-by":"crossref","unstructured":"Samson Abramsky and Achim Jung. Domain theory. In S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, editors,Handbook of Logic in Computer Science, volume 3, pages 1-168. 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