{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,30]],"date-time":"2023-09-30T09:12:01Z","timestamp":1696065121455},"reference-count":24,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2017,12,5]],"date-time":"2017-12-05T00:00:00Z","timestamp":1512432000000},"content-version":"vor","delay-in-days":4,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In set theory without the axiom of choice <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500087-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500087:malq201500087-math-0001\" \/>, three\u2010space type results for the Hahn\u2010Banach property are provided. We deduce that for every Hausdorff compact scattered space <jats:italic>K<\/jats:italic>, the Banach space C(<jats:italic>K<\/jats:italic>) of real continuous functions on <jats:italic>K<\/jats:italic> satisfies the (multiple) continuous Hahn\u2010Banach property in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500087-math-0002.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500087:malq201500087-math-0002\" \/>. We also prove in <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201500087-math-0003.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201500087:malq201500087-math-0003\" \/> Rudin's theorem: \u201cRadon measures on Hausdorff compact scattered spaces are discrete\u201d.<\/jats:p>","DOI":"10.1002\/malq.201500087","type":"journal-article","created":{"date-parts":[[2017,12,5]],"date-time":"2017-12-05T12:00:24Z","timestamp":1512475224000},"page":"320-333","source":"Crossref","is-referenced-by-count":0,"title":["Three\u2010space type Hahn\u2010Banach properties"],"prefix":"10.1002","volume":"63","author":[{"given":"Marianne","family":"Morillon","sequence":"first","affiliation":[{"name":"Laboratoire d'Informatique et de Math\u00e9matiques Universit\u00e9 de la R\u00e9union Parc Technologique Universitaire, B\u00e2timent 2, 2 rue Joseph Wetzell 97490 Sainte Clotilde France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2017,12,5]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1090\/S0002-9947-1979-0542870-6","article-title":"Injectivity, projectivity and the axiom of choice","volume":"255","author":"Blass A.","year":"1979","journal-title":"Trans. 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