{"id":25375,"date":"2021-10-14T13:18:35","date_gmt":"2021-10-14T11:18:35","guid":{"rendered":"https:\/\/cio.umh.es\/?p=25375"},"modified":"2022-01-14T13:19:16","modified_gmt":"2022-01-14T12:19:16","slug":"ferrando-j-c-saxon-s-a-2021-if-not-distinguished-is-cp-x-even-close-proceedings-of-the-american-mathematical-society-149-62583-2596-2","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2021\/10\/14\/ferrando-j-c-saxon-s-a-2021-if-not-distinguished-is-cp-x-even-close-proceedings-of-the-american-mathematical-society-149-62583-2596-2\/","title":{"rendered":"Ferrando, J.C., Saxon, S.A. (2021) \u00abIf not distinguished, is cp (x) even close?\u00bb, Proceedings of the American Mathematical Society, 149 (6):2583\u20132596"},"content":{"rendered":"<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong style=\"font-size: 18px\">Juan Carlos Ferrando (Operations Research Center, University Miguel Hern\u00e1ndez of Elche) and Stephen A. Saxon (Department of Mathematics, University of Florida)<\/strong><\/p>\n<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Abstract: <\/strong>Cp (X) is distinguished \u2192the strong dual L\u03b2 (X) is barrelled \u2192 the strong bidual M (X) = RX. So one may judge how nearly distinguished Cp (X) is by how nearly barrelled L\u03b2 (X) is, and also by how near the dense subspace M (X) is to the Baire space RX. Being Baire-like, M (X) is always fairly close to RX in that sense. But if Cp (X) is not distinguished, we show the codimension of M (X) is uncountable, i.e., M (X) is algebraically far from RX, andmoreover, L\u03b2 (X) is very far from barrelled, not even primitive. Thus we profile weak barrelledness for L\u03b2 (X) and M (X) spaces. At the same time, we characterize those Tychonoff spaces X for which Cp (X) is distinguished, solving the original problem from our series of papers.<\/p>","protected":false},"excerpt":{"rendered":"<p>Juan Carlos Ferrando (Operations Research Center, University Miguel Hern\u00e1ndez of Elche) and Stephen A. Saxon (Department of Mathematics, University of Florida)<br \/>\nAbstract: Cp (X) is distinguished \u2192the strong dual L\u03b2 (X) is barrelled \u2192 the strong bidual M (X) = RX. So one may judge how nearly distinguished Cp (X) is by how nearly barrelled L\u03b2 [&#8230;]<\/p>","protected":false},"author":5675,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[369888],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25375"}],"collection":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/users\/5675"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=25375"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25375\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=25375"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=25375"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=25375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}