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Since left resp. right adjoint maps are the residuated resp. residual maps (having the property that preimages of principal downsets resp. upsets are again such), one may not only regard the l-morphisms as abstract continuous maps in a pointfree framework (as familiar in the complete case), but also characterize them by concrete closure-theoretical continuity properties. These concepts apply to locales (frames, complete Heyting lattices) and provide generalizations of continuous and open maps between spaces to an algebraic (not necessarily complete) pointfree setting.<\/jats:p>","DOI":"10.1007\/s00012-022-00767-4","type":"journal-article","created":{"date-parts":[[2022,3,19]],"date-time":"2022-03-19T13:02:36Z","timestamp":1647694956000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Adjoint maps between implicative semilattices and continuity of localic maps"],"prefix":"10.1007","volume":"83","author":[{"given":"Marcel","family":"Ern\u00e9","sequence":"first","affiliation":[]},{"given":"Jorge","family":"Picado","sequence":"additional","affiliation":[]},{"given":"Ale\u0161","family":"Pultr","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,19]]},"reference":[{"key":"767_CR1","volume-title":"Abstract and Concrete Categories. 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