{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:06:09Z","timestamp":1775462769319,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2003,1,17]],"date-time":"2003-01-17T00:00:00Z","timestamp":1042761600000},"content-version":"unspecified","delay-in-days":47,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2002,12]]},"abstract":"<jats:p>There are two main approaches to obtaining \u2018topological\u2019 cartesian-closed categories. Under \none approach, one restricts to a full subcategory of topological spaces that happens to be \ncartesian closed \u2013 for example, the category of <jats:italic>sequential<\/jats:italic> spaces. Under the other, one \ngeneralises the notion of space \u2013 for example, to Scott's notion of <jats:italic>equilogical<\/jats:italic> space. In this \npaper, we show that the two approaches are equivalent for a large class of objects. We first \nobserve that the category of countably based equilogical spaces has, in a precisely defined \nsense, a largest full subcategory that can be simultaneously viewed as a full subcategory of \ntopological spaces. In fact, this category turns out to be equivalent to the category of all \nquotient spaces of countably based topological spaces. We show that the category is \nbicartesian closed with its structure inherited, on the one hand, from the category of \nsequential spaces, and, on the other, from the category of equilogical spaces. \nWe also show that the category of countably based equilogical spaces has a larger full \nsubcategory that can be simultaneously viewed as a full subcategory of <jats:italic>limit spaces<\/jats:italic>. This full \nsubcategory is locally cartesian closed and the embeddings into limit spaces and countably \nbased equilogical spaces preserve this structure. We observe that it seems essential to go \nbeyond the realm of topological spaces to achieve this result.<\/jats:p>","DOI":"10.1017\/s0960129502003699","type":"journal-article","created":{"date-parts":[[2003,2,7]],"date-time":"2003-02-07T09:15:20Z","timestamp":1044609320000},"page":"739-770","source":"Crossref","is-referenced-by-count":16,"title":["Topological and limit-space subcategories of countably-based equilogical spaces"],"prefix":"10.1017","volume":"12","author":[{"given":"MAT\u00cdAS","family":"MENNI","sequence":"first","affiliation":[]},{"given":"ALEX","family":"SIMPSON","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2003,1,17]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129502003699","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T20:09:08Z","timestamp":1557173348000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129502003699\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2002,12]]}},"alternative-id":["S0960129502003699"],"URL":"https:\/\/doi.org\/10.1017\/s0960129502003699","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,12]]}}}