{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T11:20:57Z","timestamp":1769772057457,"version":"3.49.0"},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2010,1,18]],"date-time":"2010-01-18T00:00:00Z","timestamp":1263772800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:p>We introduce pairwise Stone spaces as a bitopological generalisation of Stone spaces \u2013 the duals of Boolean algebras \u2013 and show that they are exactly the bitopological duals of bounded distributive lattices. The category<jats:bold>PStone<\/jats:bold>of pairwise Stone spaces is isomorphic to the category<jats:bold>Spec<\/jats:bold>of spectral spaces and to the category<jats:bold>Pries<\/jats:bold>of Priestley spaces. In fact, the isomorphism of<jats:bold>Spec<\/jats:bold>and<jats:bold>Pries<\/jats:bold>is most naturally seen through<jats:bold>PStone<\/jats:bold>by first establishing that<jats:bold>Pries<\/jats:bold>is isomorphic to<jats:bold>PStone<\/jats:bold>, and then showing that<jats:bold>PStone<\/jats:bold>is isomorphic to<jats:bold>Spec<\/jats:bold>. We provide the bitopological and spectral descriptions of many algebraic concepts important in the study of distributive lattices. We also give new bitopological and spectral dualities for Heyting algebras, thereby providing two new alternatives to Esakia's duality.<\/jats:p>","DOI":"10.1017\/s0960129509990302","type":"journal-article","created":{"date-parts":[[2010,1,18]],"date-time":"2010-01-18T09:47:16Z","timestamp":1263808036000},"page":"359-393","source":"Crossref","is-referenced-by-count":43,"title":["Bitopological duality for distributive lattices and Heyting algebras"],"prefix":"10.1017","volume":"20","author":[{"given":"GURAM","family":"BEZHANISHVILI","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"NICK","family":"BEZHANISHVILI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DAVID","family":"GABELAIA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ALEXANDER","family":"KURZ","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,1,18]]},"reference":[{"key":"S0960129509990302_ref20","unstructured":"Jung A. and Moshier M. 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