{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T15:40:07Z","timestamp":1719070807987},"reference-count":18,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2010,1,13]],"date-time":"2010-01-13T00:00:00Z","timestamp":1263340800000},"content-version":"vor","delay-in-days":377,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2009,1]]},"abstract":"Working within a complete (not necessarily atomic) Boolean algebra, we use a sublattice to define a topology on that algebra. Our operators generalize complement<\/jats:italic> on a lattice which in turn abstracts the set theoretic operator. Less restricted than those of Banaschewski and Samuel, the operators exhibit some surprising behaviors. We consider properties of such lattices and their interrelations. Many of these properties are abstractions and generalizations of topological spaces. The approach is similar to that of Bachman and Cohen. It is in the spirit of Alexandroff, Frol\u00edk, and N\u00f6beling, although the setting is more general. Proceeding in this manner, we can handle diverse topological theorems systematically before specializing to get as corollaries as the\ntopological results of Alexandroff, Alo and Shapiro, Dykes, Frol\u00edk, and Ramsay.<\/jats:p>","DOI":"10.1155\/2009\/474356","type":"journal-article","created":{"date-parts":[[2010,1,13]],"date-time":"2010-01-13T15:30:09Z","timestamp":1263396609000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Lattice Operators and Topologies"],"prefix":"10.1155","volume":"2009","author":[{"given":"Eva","family":"Cogan","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,1,13]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1002\/mana.19630270107"},{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/1990559"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160260504"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02416957"},{"key":"e_1_2_8_5_2","first-page":"307","article-title":"Additive set-functions in abstract spaces","volume":"8","author":"Alexandroff A. 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