{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T10:17:38Z","timestamp":1780049858358,"version":"3.53.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T00:00:00Z","timestamp":1774137600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T00:00:00Z","timestamp":1774137600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-SC0011090"],"award-info":[{"award-number":["DE-SC0011090"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100020637","name":"Department of Physics, Massachusetts Institute of Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100020637","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004477","name":"Universiteit Stellenbosch","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004477","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100021099","name":"Skye Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100021099","id-type":"DOI","asserted-by":"publisher"}]},{"name":"NITheCS"},{"DOI":"10.13039\/501100003343","name":"Cambridge Trust","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003343","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Categor Struct"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s10485-025-09840-0","type":"journal-article","created":{"date-parts":[[2026,3,22]],"date-time":"2026-03-22T12:30:54Z","timestamp":1774182654000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["What is Connectivity?"],"prefix":"10.1007","volume":"34","author":[{"given":"Jean F.","family":"Du Plessis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zurab","family":"Janelidze","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernardus A.","family":"Wessels","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,3,22]]},"reference":[{"issue":"1","key":"9840_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/0022-4049(91)90003-K","volume":"70","author":"D Baboolal","year":"1991","unstructured":"Baboolal, D., Banaschewski, B.: Compactification and local connectedness of frames. J. Pure Appl. Algebra 70(1), 3\u201316 (1991)","journal-title":"J. Pure Appl. Algebra"},{"issue":"4","key":"9840_CR2","doi-asserted-by":"publisher","first-page":"548","DOI":"10.1090\/S0002-9939-1955-0072852-1","volume":"6","author":"VK Balachandran","year":"1955","unstructured":"Balachandran, V.K.: On complete lattices and a problem of Birkhoff and Frink. Proc. Am. Math. Soc. 6(4), 548\u2013553 (1955)","journal-title":"Proc. Am. Math. Soc."},{"key":"9840_CR3","unstructured":"B\u00f6rger, R.: Connectivity spaces and component categories. In: Categorical topology: Proceedings of the International Conference held at the University of Toledo, Ohio, USA, vol.\u00a05 of Sigma Ser. Pure Math. Heldermann. pp. 71\u201389 (1983)"},{"key":"9840_CR4","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1016\/S0166-8641(89)80002-1","volume":"33","author":"R B\u00f6rger","year":"1989","unstructured":"B\u00f6rger, R.: Multicoreflective subcategories and coprime objects. Topol. Appl. 33, 127\u2013142 (1989)","journal-title":"Topol. Appl."},{"key":"9840_CR5","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1024476403183","volume":"19","author":"U Braga-Neto","year":"2003","unstructured":"Braga-Neto, U., Goutsias, J.: A theoretical tour of connectivity in image processing and analysis. J. Math. Imaging Vis. 19, 5\u201331 (2003)","journal-title":"J. Math. Imaging Vis."},{"issue":"1","key":"9840_CR6","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/s11083-024-09676-8","volume":"42","author":"MM Clementino","year":"2024","unstructured":"Clementino, M.M., Janelidze, G.: Effective descent morphisms of filtered preorders. Order 42(1), 181\u201392 (2024)","journal-title":"Order"},{"key":"9840_CR7","unstructured":"Du\u00a0Plessis, J.F.: Sequence A374073, number of connected chainmails with $$n$$ unlabeled elements. Online Encyclopedia of Integer Sequences (2024). Accessed 28 Jan 2025"},{"key":"9840_CR8","unstructured":"Du\u00a0Plessis, J.F., Janelidze, Z., Rathilal, C., Wessels, B.A.: On frames and chainmails (in preperation)"},{"issue":"4","key":"9840_CR9","first-page":"282","volume":"I","author":"S Dugowson","year":"2010","unstructured":"Dugowson, S.: On connectivity spaces. Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle Cat\u00e9goriques, LI(4), 282\u2013315 (2010)","journal-title":"Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle Cat\u00e9goriques, L"},{"key":"9840_CR10","volume-title":"Categories, Allegories volume\u00a039 of Mathematical Library","author":"P Freyd","year":"1990","unstructured":"Freyd, P., Scedrov, A.: Categories, Allegories. Volume\u00a039 of Mathematical Library. Elsevier, North-Holland (1990)"},{"issue":"3","key":"9840_CR11","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/BF02909632","volume":"17","author":"PC Hammer","year":"1968","unstructured":"Hammer, P.C., Singletary, W.E.: Connectedness-equivalent spaces on the line. Rendiconti del Circolo Matematico di Palermo 17(3), 343\u2013355 (1968)","journal-title":"Rendiconti del Circolo Matematico di Palermo"},{"key":"9840_CR12","series-title":"The University Series in Higher Mathematics","volume-title":"General Topology","author":"JL Kelley","year":"1955","unstructured":"Kelley, J.L.: General Topology. The University Series in Higher Mathematics, D.\u00a0van\u00a0Nostrand Company Inc., New York (1955)"},{"key":"9840_CR13","unstructured":"Matheron, G.: Remarques sur les fermetures-partitions. International report, Centre de G\u00e9ostatistique et de Morphologie Math\u00e9matique, Ecole des Mines de Paris (1985)"},{"key":"9840_CR14","first-page":"141","volume-title":"Image Analysis and Mathematical Morphology","author":"G Matheron","year":"1988","unstructured":"Matheron, G., Serra, J.: Strong filters and connectivity. In: Serra, J. (ed.) Image Analysis and Mathematical Morphology, vol. 2, pp. 141\u2013157. Academic Press, London (1988)"},{"key":"9840_CR15","first-page":"1","volume":"39","author":"J Muscat","year":"2006","unstructured":"Muscat, J., Buhagiar, D.: Connective spaces. Mem. Fac. Sci. Eng. Shimane Univ. B 39, 1\u201313 (2006)","journal-title":"Mem. Fac. Sci. Eng. Shimane Univ. B"},{"key":"9840_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0154-6","volume-title":"Frames and Locales: Topology Without Points","author":"J Picado","year":"2012","unstructured":"Picado, J., Pultr, A.: Frames and Locales: Topology Without Points. Springer, Cham (2012)"},{"issue":"3","key":"9840_CR17","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1023\/A:1008324520475","volume":"9","author":"J Serra","year":"1998","unstructured":"Serra, J.: Connectivity on complete lattices. J. Math. Imaging Vis. 9(3), 231\u2013251 (1998)","journal-title":"J. Math. Imaging Vis."},{"issue":"4","key":"9840_CR18","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/s11786-015-0241-1","volume":"9","author":"BMR Stadler","year":"2015","unstructured":"Stadler, B.M.R., Stadler, P.F.: Connectivity spaces. Math. Comput. Sci. 9(4), 409\u2013436 (2015)","journal-title":"Math. Comput. Sci."},{"issue":"3","key":"9840_CR19","doi-asserted-by":"publisher","first-page":"687","DOI":"10.2307\/1969257","volume":"42","author":"AD Wallace","year":"1941","unstructured":"Wallace, A.D.: Separation spaces. Ann. Math. 42(3), 687\u2013697 (1941)","journal-title":"Ann. Math."}],"container-title":["Applied Categorical Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-025-09840-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10485-025-09840-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-025-09840-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T09:59:20Z","timestamp":1780048760000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10485-025-09840-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,22]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["9840"],"URL":"https:\/\/doi.org\/10.1007\/s10485-025-09840-0","relation":{},"ISSN":["0927-2852","1572-9095"],"issn-type":[{"value":"0927-2852","type":"print"},{"value":"1572-9095","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,22]]},"assertion":[{"value":"13 April 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 November 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 March 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"18"}}