{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:35:06Z","timestamp":1753889706201,"version":"3.41.2"},"reference-count":42,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2011,10,26]],"date-time":"2011-10-26T00:00:00Z","timestamp":1319587200000},"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>In this paper, for a given sequentially Yoneda-complete T_1 quasi-metric\nspace (X,d), the domain theoretic models of the hyperspace K_0(X) of nonempty\ncompact subsets of (X,d) are studied. To this end, the $\\omega$-Plotkin domain\nof the space of formal balls BX, denoted by CBX is considered. This domain is\ngiven as the chain completion of the set of all finite subsets of BX with\nrespect to the Egli-Milner relation. Further, a map $\\phi:K_0(X)\\rightarrow\nCBX$ is established and proved that it is an embedding whenever K_0(X) is\nequipped with the Vietoris topology and respectively CBX with the Scott\ntopology. Moreover, if any compact subset of (X,d) is d^{-1}-precompact, \\phi\nis an embedding with respect to the topology of Hausdorff quasi-metric H_d on\nK_0(X). Therefore, it is concluded that (CBX,\\sqsubseteq,\\phi) is an\n$\\omega$-computational model for the hyperspace K_0(X) endowed with the\nVietoris and respectively the Hausdorff topology. Next, an algebraic\nsequentially Yoneda-complete quasi-metric D on CBX$ is introduced in such a way\nthat the specialization order $\\sqsubseteq_D$ is equivalent to the usual\npartial order of CBX and, furthermore, $\\phi:({\\cal\nK}_0(X),H_d)\\rightarrow({\\bf C}{\\bf B}X,D)$ is an isometry. This shows that\n(CBX,\\sqsubseteq,\\phi,D) is a quantitative $\\omega$-computational model for\n(K_(X),H_d).<\/jats:p>","DOI":"10.2168\/lmcs-7(4:1)2011","type":"journal-article","created":{"date-parts":[[2012,6,20]],"date-time":"2012-06-20T09:05:51Z","timestamp":1340183151000},"source":"Crossref","is-referenced-by-count":0,"title":["Computational Models of Certain Hyperspaces of Quasi-metric Spaces"],"prefix":"10.46298","volume":"Volume 7, Issue 4","author":[{"given":"Massoud","family":"Pourmahdian","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mahdi","family":"Ali-Akbari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2011,10,26]]},"reference":[{"key":"10.2168\/LMCS-7(4:1)2011_abramsky","unstructured":"S. Abramsky and A. Jung. Domain theory. in: S. Abramsky, D.M. Gabbay, T.S.E. 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