{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T12:07:21Z","timestamp":1773576441536,"version":"3.50.1"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"published-print":{"date-parts":[[2016,3,24]]},"abstract":"<jats:p>It is well known that a locale is subfit iff each of its open sublocales is a join of closed ones, and fit iff each of its closed sublocales is a meet of open ones. This formulation, however, exaggerates the parallelism between the behavior of fitness and subfitness. For it can be shown that a locale is fit iff each of its sublocales is a meet of closed ones, but it is not the case that a locale is subfit iff each of its sublocales is a join of closed ones. Thus we are led to take up the very natural question of which locales have the feature that every sublocale is a join of closed sublocales. In this note we show that these are precisely the subfit locales which are scattered in the point-free sense of [13], and we add a variation for spatial frames.<\/jats:p>","DOI":"10.4171\/pm\/1980","type":"journal-article","created":{"date-parts":[[2016,3,24]],"date-time":"2016-03-24T18:45:06Z","timestamp":1458845106000},"page":"139-152","source":"Crossref","is-referenced-by-count":11,"title":["On an aspect of scatteredness in the point-free setting"],"prefix":"10.4171","volume":"73","author":[{"given":"Richard N.","family":"Ball","sequence":"first","affiliation":[{"name":"University of Denver, USA"}]},{"given":"Jorge","family":"Picado","sequence":"additional","affiliation":[{"name":"Universidade de Coimbra, Portugal"}]},{"given":"Ale\u0161","family":"Pultr","sequence":"additional","affiliation":[{"name":"Charles University, Prague, Czech Republic"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/PM\/1980","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T13:12:39Z","timestamp":1762261959000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/1980"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,24]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.4171\/pm\/1980","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"value":"0032-5155","type":"print"},{"value":"1662-2758","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,24]]}}}