{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T19:42:21Z","timestamp":1694979741341},"reference-count":18,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2018,7,17]],"date-time":"2018-07-17T00:00:00Z","timestamp":1531785600000},"content-version":"vor","delay-in-days":16,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A function from Baire space <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201700015-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201700015:malq201700015-math-0001\" \/> to the natural numbers <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201700015-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201700015:malq201700015-math-0002\" \/> is called formally continuous if it is induced by a morphism between the corresponding formal spaces. We compare formal continuity to two other notions of continuity on Baire space working in Bishop constructive mathematics: one is a function induced by a Brouwer\u2010operation (i.e., inductively defined neighbourhood function); the other is a function uniformly continuous near every compact image. We show that formal continuity is equivalent to the former while it is strictly stronger than the latter. The equivalence of formally continuous functions and those induced by Brouwer\u2010operations requires Countable Choice.<\/jats:p>","DOI":"10.1002\/malq.201700015","type":"journal-article","created":{"date-parts":[[2018,7,17]],"date-time":"2018-07-17T13:11:37Z","timestamp":1531833097000},"page":"192-200","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Formally continuous functions on Baire space"],"prefix":"10.1002","volume":"64","author":[{"given":"Tatsuji","family":"Kawai","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica Universit\u00e0 di Padova via Trieste 63 35121 Padova Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,7,17]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2005.05.016"},{"key":"e_1_2_7_3_1","unstructured":"P.AczelandM.Rathjen Notes on constructive set theory Tech. Rep. 40 Institut Mittag\u2010Leffler (2000\/2001)."},{"key":"e_1_2_7_4_1","volume-title":"Foundations of Constructive Analysis, McGraw\u2010Hill Series in Higher Mathematics","author":"Bishop E.","year":"1967"},{"key":"e_1_2_7_5_1","volume-title":"Constructive Functional Analysis, Research Notes in Mathematics","author":"Bridges D.","year":"1979"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2011.06.018"},{"key":"e_1_2_7_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01447860"},{"key":"e_1_2_7_8_1","doi-asserted-by":"crossref","unstructured":"M. P.FourmanandR. J.Grayson Formal spaces in: The L.E.J. Brouwer Centenary Symposium: proceedings of the conference held in Noordwijkerhout 8\u201313 June 1981 edited byA. S.TroelstraandD. vanDalen Studies in Logic and the Foundations of Mathematics Vol. 110 (North\u2010Holland 1982) pp.107\u2013122.","DOI":"10.1016\/S0049-237X(09)70126-0"},{"key":"e_1_2_7_9_1","doi-asserted-by":"crossref","unstructured":"M. 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G.Skordev(Springer 1987) pp.187\u2013204.","DOI":"10.1007\/978-1-4613-0897-3_12"},{"key":"e_1_2_7_16_1","volume-title":"Constructivism in Mathematics: An Introduction. Volume I, Studies in Logic and the Foundations of Mathematics","author":"Troelstra A. S.","year":"1988"},{"key":"e_1_2_7_17_1","volume-title":"Constructivism in Mathematics: An Introduction. Volume II, Studies in Logic and the Foundations of Mathematics","author":"Troelstra A. S.","year":"1988"},{"key":"e_1_2_7_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2012.01.010"},{"issue":"15","key":"e_1_2_7_19_1","first-page":"328","article-title":"Localic completion of generalized metric spaces I","volume":"14","author":"Vickers S.","year":"2005","journal-title":"Theory Appl. 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