{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:43:28Z","timestamp":1740123808636,"version":"3.37.3"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T00:00:00Z","timestamp":1643846400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T00:00:00Z","timestamp":1643846400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Order"],"published-print":{"date-parts":[[2023,4]]},"DOI":"10.1007\/s11083-021-09580-5","type":"journal-article","created":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T06:03:47Z","timestamp":1643868227000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Subordinations on Bounded Distributive Lattices"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2542-4128","authenticated-orcid":false,"given":"Sergio A.","family":"Celani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,2,3]]},"reference":[{"key":"9580_CR1","first-page":"93","volume":"5","author":"PS Aleksandrov","year":"1959","unstructured":"Aleksandrov, P. S., Ponomarev, V. I.: Compact extensions of topological spaces (Russian) . Vestnik Moskov Univ. Ser. Mat. Meh. Astr. Fiz. Him. 5, 93\u2013108 (1959)","journal-title":"Vestnik Moskov Univ. Ser. Mat. Meh. Astr. Fiz. Him."},{"issue":"1-3","key":"9580_CR2","first-page":"29","volume":"81","author":"Ph Balbiani","year":"2007","unstructured":"Balbiani, P. h., Tinchev, T., Vakarelov, D.: Modal logics for region-based theories of space. Fund Inform. 81(1-3), 29\u201382 (2007)","journal-title":"Fund Inform."},{"key":"9580_CR3","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1002\/mana.19901490107","volume":"149","author":"B Banaschewski","year":"1990","unstructured":"Banaschewski, B.: Compactification of frames. Math. Nachr. 149, 105\u2013115 (1990)","journal-title":"Math. Nachr."},{"key":"9580_CR4","doi-asserted-by":"publisher","first-page":"1064","DOI":"10.1016\/j.topol.2010.01.007","volume":"157","author":"G Bezhanishvili","year":"2010","unstructured":"Bezhanishvili, G.: Stone duality and Gleason covers through de Vries duality. Topol. Appl. 157, 1064\u20131080 (2010)","journal-title":"Topol. Appl."},{"issue":"4","key":"9580_CR5","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s00012-013-0253-0","volume":"70","author":"G Bezhanishvili","year":"2013","unstructured":"Bezhanishvili, G.: Lattice subordinations and Priestley duality. Algebra Univ. 70(4), 359\u2013377 (2013)","journal-title":"Algebra Univ."},{"issue":"3","key":"9580_CR6","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/s00012-013-0247-y","volume":"70","author":"G Bezhanishvili","year":"2013","unstructured":"Bezhanishvili, G., Gabelaia, D., Jibladze, M.: Funayama\u2019s theorem revisited. Algebra Univ. 70(3), 271\u2013286 (2013)","journal-title":"Algebra Univ."},{"issue":"01","key":"9580_CR7","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1017\/jsl.2015.54","volume":"81","author":"G Bezhanishvili","year":"2016","unstructured":"Bezhanishvili, G., Bezhanishvili, N., Iemhoff, R.: Stable canonical rules. J. Symb. Log. 81(01), 284\u2013315 (2016)","journal-title":"J. Symb. Log."},{"key":"9580_CR8","doi-asserted-by":"crossref","unstructured":"Bezhanishvili, G., Bezhanishvili, N., Sourabh, S., Venema, Y.: Irreducible Equivalence Relations, Gleason Spaces, and de Vries Duality. Appl. Categ. Struct., 1\u201326 (2016)","DOI":"10.1007\/s10485-016-9434-2"},{"key":"9580_CR9","doi-asserted-by":"crossref","unstructured":"Bezhanishvili, G, Bezhanishvili, N, Santoli, T, Venema, Y.: A strict implication calculus for compact Hausdorff spaces. Ann. Pure Appl. Log. 170(11) (November 2019)","DOI":"10.1016\/j.apal.2019.06.003"},{"key":"9580_CR10","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/s10485-013-9308-9","volume":"22","author":"G Bezhanishvili","year":"2014","unstructured":"Bezhanishvili, G., Harding, J.: Proximity frames and regularization. Appl. Categ. Struct. 22, 43\u201378 (2014)","journal-title":"Appl. Categ. Struct."},{"issue":"1","key":"9580_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1093\/logcom\/exs030","volume":"25","author":"G Bezhanishvili","year":"2015","unstructured":"Bezhanishvili, G., Bezhanishvili, N., Harding, J.: Modal compact Hausdorff spaces. J. Log. Comput. 25(1), 1\u201335 (2015)","journal-title":"J. Log. Comput."},{"key":"9580_CR12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884","volume-title":"Modal Logic","author":"P Blackburn","year":"2001","unstructured":"Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)"},{"key":"9580_CR13","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/s11083-004-6449-3","volume":"21","author":"J Castro","year":"2004","unstructured":"Castro, J., Celani, S. A.: Quasi-modal lattices. Order 21, 107\u2013129 (2004)","journal-title":"Order"},{"key":"9580_CR14","unstructured":"Celani S. A.: Precontact relations and quasi-modal operators in Boolean algebras. Actas del XIII Congreso Dr. Antonio Monteiro, Univ. Nac. del Sur, 2016, pp. 63\u201379. Available in http:\/\/inmabb-conicet.gob.ar\/publicaciones\/actas-del-congreso-monteiro\/13(2016)"},{"issue":"1","key":"9580_CR15","first-page":"41","volume":"50","author":"SA Celani","year":"2009","unstructured":"Celani, S. A.: Amalgamation Property in Quasi-Modal algebras. Rev. Uni\u00f3n Mat. Argentina 50(1), 41\u201346 (2009)","journal-title":"Rev. Uni\u00f3n Mat. Argentina"},{"key":"9580_CR16","doi-asserted-by":"crossref","unstructured":"Celani S. A.: Simple and subdirectly irreducibles bounded distributive lattices with unary operators. International Journal of Mathematics and Mathematical Sciences Volume 2006, Article ID 21835, pp. 20 (2006)","DOI":"10.1155\/IJMMS\/2006\/21835"},{"key":"9580_CR17","first-page":"119","volume":"2","author":"SA Celani","year":"2005","unstructured":"Celani, S. A.: Subdirectly irreducible quasi-modal algebras. Acta Mat. Univ. Comenianae 2, 119\u2013228 (2005)","journal-title":"Acta Mat. Univ. Comenianae"},{"issue":"4","key":"9580_CR18","doi-asserted-by":"publisher","first-page":"721","DOI":"10.21136\/MB.2001.134115","volume":"126","author":"SA Celani","year":"2001","unstructured":"Celani, S. A.: Quasi-modal algebras. Math. Bohem. 126(4), 721\u2013736 (2001)","journal-title":"Math. Bohem."},{"key":"9580_CR19","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1002\/malq.19990450206","volume":"45","author":"SA Celani","year":"1999","unstructured":"Celani, S. A.: Distributive lattices with a negation operator. Math. Log. Q. 45, 207\u2013218 (1999)","journal-title":"Math. Log. Q."},{"issue":"3","key":"9580_CR20","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/BF00383451","volume":"8","author":"R Cignoli","year":"1991","unstructured":"Cignoli, R., Lafalce, S., Petrovich, A.: Remarks on Priestley duality for distributive lattices. Order 8(3), 299\u2013315 (1991)","journal-title":"Order"},{"key":"9580_CR21","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809088","volume-title":"Introduction to Lattices and Order","author":"B Davey","year":"2002","unstructured":"Davey, B., Priestley, H.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002). https:\/\/doi.org\/10.1017\/CBO9780511809088","edition":"2nd edn."},{"key":"9580_CR22","unstructured":"de Vries, H.: Compact Spaces and Compactifications. an Algebraic Approach. PhD thesis, University of Amsterdam (1962)"},{"issue":"15","key":"9580_CR23","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.topol.2017.01.019","volume":"227","author":"G Dimov","year":"2017","unstructured":"Dimov, G., Vakarelov, D.: Topological representation of precontact algebras and a connected version of the Stone Duality Theorem-I. Topol. Appl. 227 (15), 64\u2013101 (2017)","journal-title":"Topol. Appl."},{"key":"9580_CR24","doi-asserted-by":"crossref","unstructured":"Dimov G., Vakarelov D.: Topological representation of precontact algebras. In: Mac-Caull, W., Winter, M., D\u00fcntsch, I. (eds.) Relational Methods in Computer Science, volume 3929 of Lecture Notes in Computer Science, pp 1\u201316. Springer, Berlin (2006)","DOI":"10.1007\/11734673_1"},{"key":"9580_CR25","doi-asserted-by":"crossref","unstructured":"D\u00fcntsch, I., MacCaull, W., Vakarelov, D., Winter, M.: Distributive contact lattices: Topological representation. J. Log. Algebraic Program. 76, 18\u201334 (2008)","DOI":"10.1016\/j.jlap.2007.10.002"},{"key":"9580_CR26","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1016\/j.tcs.2005.06.030","volume":"347","author":"I D\u00fcntsch","year":"2005","unstructured":"D\u00fcntsch, I., Winter, M.: A representation theorem for Boolean contact algebras. Theor. Comput. Sci. (B) 347, 498\u2013512 (2005)","journal-title":"Theor. Comput. Sci. (B)"},{"issue":"1-4","key":"9580_CR27","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10472-007-9064-3","volume":"49","author":"I D\u00fcntsch","year":"2007","unstructured":"D\u00fcntsch, I., Vakarelov, D.: Region-based theory of discrete spaces: a proximity approach. Ann. Math. Artif. Intell. 49(1-4), 5\u201314 (2007)","journal-title":"Ann. Math. Artif. Intell."},{"key":"9580_CR28","doi-asserted-by":"crossref","unstructured":"El-Zawawy M. A., Jung, A.: Priestley Duality for Strong Proximity Lattices.: Electronic Notes in Theoretical Computer Science 158, 199\u2013217 (2006)","DOI":"10.1016\/j.entcs.2006.04.011"},{"issue":"2","key":"9580_CR29","first-page":"207","volume":"40","author":"M Gehrke","year":"1994","unstructured":"Gehrke, M., J\u00f3nsson, B.: Bounded distributive lattices with operators. Math. Japon. 40(2), 207\u2013215 (1994)","journal-title":"Math. Japon."},{"key":"9580_CR30","doi-asserted-by":"crossref","unstructured":"Gierz, G., Keimel, K.: Continuous ideal completions and compactifications, Continuous lattices. proceedings, Bremen 1979, Lecture Notes in Mathematics, vol. 871, pp. 97\u2013124. Springer, Berlin (1981)","DOI":"10.1007\/BFb0089905"},{"key":"9580_CR31","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511542725","volume-title":"Continuous Lattices and Domains","author":"G Gierz","year":"2003","unstructured":"Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M., Scott, D. S.: Continuous Lattices and Domains. Cambridge University Press, Cambridge (2003)"},{"key":"9580_CR32","doi-asserted-by":"crossref","unstructured":"Goubault-Larrecq, J.: Non-hausdorff topology and domain theory: Selected topics in point-set topology, Vol. 22. Cambridge University Press (2013)","DOI":"10.1017\/CBO9781139524438"},{"key":"9580_CR33","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10472-016-9499-5","volume":"77","author":"T Ivanova","year":"2016","unstructured":"Ivanova, T., Vakarelov, D.: Distributive mereotopology: extended distributive contact lattices. Ann. Math. Artif. Intell. 77, 3\u201341 (2016)","journal-title":"Ann. Math. Artif. Intell."},{"key":"9580_CR34","volume-title":"Stone Spaces","author":"PT Johnstone","year":"1982","unstructured":"Johnstone, P. T.: Stone Spaces. Cambridge University Press, Cambridge (1982)"},{"key":"9580_CR35","doi-asserted-by":"crossref","unstructured":"Jung, A., S\u00fcnderhauf, P.: On the duality of compact vs. open. In: Papers on General Topology and Applications (Gorham, ME, 1995), pp. 214\u2013230. New York Acad. Sci., New York","DOI":"10.1111\/j.1749-6632.1996.tb49171.x"},{"key":"9580_CR36","volume-title":"Proximity Spaces","author":"SA Naimpally","year":"1970","unstructured":"Naimpally, S. A., Warrack, D.: Proximity Spaces. Cambridge University Press, Cambridge (1970)"},{"key":"9580_CR37","doi-asserted-by":"crossref","unstructured":"Ono, H.: On some intuitionistic modal logics. Publ. Res. Inst. Math. Sci. 13(3), 687\u2013722 (1977\/78)","DOI":"10.2977\/prims\/1195189604"},{"key":"9580_CR38","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1112\/blms\/2.2.186","volume":"2","author":"HA Priestley","year":"1970","unstructured":"Priestley, H. A.: Representation of distributive lattices by means of ordered Stone spaces. Bull. Lond. Math. Soc. 2, 186\u2013190 (1970)","journal-title":"Bull. Lond. Math. Soc."},{"key":"9580_CR39","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1112\/plms\/s3-24.3.507","volume":"3","author":"HA Priestley","year":"1972","unstructured":"Priestley, H. A.: Ordered topological spaces and the representation of distributive lattices. Proc. Lond. Math. Soc. 3, 507\u2013530 (1972)","journal-title":"Proc. Lond. Math. Soc."},{"key":"9580_CR40","unstructured":"Pultr, A., Sichler, J.: Frames in Priestley\u2019s duality, Cahiers de Top. et g\u00e9om. Diff. Cat. XXIX-3, pp. 193\u2013202 (1988)"},{"key":"9580_CR41","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1112\/jlms\/s2-45.2.321","volume":"45","author":"MB Smyth","year":"1992","unstructured":"Smyth, M. B.: Stable compactification I. J. Lond. Math. Soc. 45, 321\u2013340 (1992)","journal-title":"J. Lond. Math. Soc."},{"key":"9580_CR42","doi-asserted-by":"crossref","unstructured":"Vakarelov, D.: Region-Based Theory of Space: Algebras of Regions, Representation Theory, and Logics. In: Gabbay, D., Goncharov, S., Zakharyaschev, M. (eds.) Mathematical Problems from Applied Logic, vol. 2, pp 267\u2013348. Springer, Heidelberg (2007)","DOI":"10.1007\/978-0-387-69245-6_6"},{"key":"9580_CR43","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1016\/j.topol.2011.09.040","volume":"159","author":"SJ van Gool","year":"2012","unstructured":"van Gool, S. J.: Duality and canonical extensions for stably compact spaces. Topol. Appl. 159, 341\u2013359 (2012)","journal-title":"Topol. Appl."},{"key":"9580_CR44","first-page":"41","volume":"17","author":"A Ward","year":"1974","unstructured":"Ward, A.: Representations of proximity lattices. Ann. Univ. Sci. Budapest. Eotvos Sect. Math. 17, 41\u201357 (1974)","journal-title":"Ann. Univ. Sci. Budapest. Eotvos Sect. Math."}],"container-title":["Order"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-021-09580-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11083-021-09580-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-021-09580-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,24]],"date-time":"2023-06-24T11:47:16Z","timestamp":1687607236000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11083-021-09580-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,3]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["9580"],"URL":"https:\/\/doi.org\/10.1007\/s11083-021-09580-5","relation":{},"ISSN":["0167-8094","1572-9273"],"issn-type":[{"type":"print","value":"0167-8094"},{"type":"electronic","value":"1572-9273"}],"subject":[],"published":{"date-parts":[[2022,2,3]]},"assertion":[{"value":"21 August 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 September 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}