{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:29:53Z","timestamp":1753882193773,"version":"3.41.2"},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,5,14]],"date-time":"2006-05-14T00:00:00Z","timestamp":1147564800000},"content-version":"vor","delay-in-days":133,"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":[[2006,1]]},"abstract":"<jats:p>It is certainly well known that a mapping between metric spaces is\ncontinuous if and only if it preserves convergent sequences. Does\nthere exist a comparable characterization for the mapping to be\nopen? Of course, the inverse mapping is set\u2010valued, in general. In\nthis research\/expository note, we show that a mapping is open if\nand only if the set\u2010valued inverse mapping preserves convergent\nsequences in an appropriate set\u2010theoretic sense.<\/jats:p>","DOI":"10.1155\/ijmms\/2006\/76162","type":"journal-article","created":{"date-parts":[[2006,6,20]],"date-time":"2006-06-20T09:35:51Z","timestamp":1150796151000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A characterization of open mapping in terms of convergent sequences"],"prefix":"10.1155","volume":"2006","author":[{"given":"Irwin E.","family":"Schochetman","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,5,14]]},"reference":[{"key":"e_1_2_1_1_2","doi-asserted-by":"crossref","unstructured":"Beer Topologies on Closed and Closed Convex Sets 1993 Kluwer Academic Dordrecht 268 Mathematics and Its Applications.","DOI":"10.1007\/978-94-015-8149-3"},{"key":"e_1_2_1_2_2","unstructured":"Berge Topological Spaces 1963 Oliver and Boyd London."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002\u20109939\u201002\u201006472\u20109"},{"key":"e_1_2_1_4_2","first-page":"319","article-title":"Notes on quotient maps","volume":"7","author":"H\u00e1jek","year":"1966","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"e_1_2_1_5_2","unstructured":"Hausdorff Set Theory 1957 Chelsea New York."},{"key":"e_1_2_1_6_2","unstructured":"KleinandThompsonA. C. Theory of Correspondences 1984 John Wiley & Sons New York Canadian Mathematical Society Series of Monographs and Advanced Texts."},{"key":"e_1_2_1_7_2","unstructured":"KolmogorovA. N.andFominS. V. Elements of the Theory of Functions and Functional Analysis. Vol. 1. Metric and Normed Spaces 1957 Graylock Press New York."},{"key":"e_1_2_1_8_2","unstructured":"Kuratowski Topology. Vol. I 1966 Academic Press New York."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2004.04.005"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2006\/076162.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/IJMMS\/2006\/76162","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T21:04:31Z","timestamp":1717707871000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/IJMMS\/2006\/76162"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1155\/IJMMS\/2006\/76162"],"URL":"https:\/\/doi.org\/10.1155\/ijmms\/2006\/76162","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2006,1]]},"assertion":[{"value":"2006-05-14","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"076162"}}