{"id":25357,"date":"2021-10-14T13:02:16","date_gmt":"2021-10-14T11:02:16","guid":{"rendered":"https:\/\/cio.umh.es\/?p=25357"},"modified":"2022-01-14T13:06:39","modified_gmt":"2022-01-14T12:06:39","slug":"ferrando-j-c-ka%cc%a7kol-j-leiderman-a-saxon-s-a-2021-distinguished-cpx-spaces-revista-de-la-real-academia-de-ciencias-exactas-fisicas-y-naturales-serie-a-matematicas-115-1","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2021\/10\/14\/ferrando-j-c-ka%cc%a7kol-j-leiderman-a-saxon-s-a-2021-distinguished-cpx-spaces-revista-de-la-real-academia-de-ciencias-exactas-fisicas-y-naturales-serie-a-matematicas-115-1\/","title":{"rendered":"Ferrando, J.C., Ka\u0327kol, J., Leiderman, A., Saxon, S.A. (2021) \u00abDistinguished Cp(X) spaces\u00bb, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales &#8211; Serie A: Matematicas, 115 (1): 27"},"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), Jerzy K\u0105kol (Faculty of Mathematics and Informatics, A. Mickiewicz University, Poznan), Arkady G.\u00a0 Leiderman (Ben-Gurion University of the Negev, Beer Sheba) 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>We continue our initial study of Cp(X) spaces that are distinguished, equiv., are large subspaces of RX, equiv., whose strong duals L\u03b2(X) carry the strongest locally convex topology. Many are distinguished, many are not. All L\u03b2(X) spaces are, as are all metrizable Cp(X) and Ck(X) spaces. To prove a space Cp(X) is not distinguished, we typically compare the character of L\u03b2(X) with |X|. A certain covering for X we call a scant cover is used to find distinguished Cp(X) spaces. Two of the main results are: (i) Cp(X) is distinguished if and only if its bidual E coincides with RX, and (ii) for a Corson compact space X, the space Cp(X) is distinguished if and only if X is scattered and Eberlein compact.<\/p>","protected":false},"excerpt":{"rendered":"<p>Juan Carlos Ferrando (Operations Research Center, University Miguel Hern\u00e1ndez of Elche), Jerzy K\u0105kol (Faculty of Mathematics and Informatics, A. Mickiewicz University, Poznan), Arkady G.\u00a0 Leiderman (Ben-Gurion University of the Negev, Beer Sheba) and Stephen A. Saxon (Department of Mathematics, University of Florida)<br \/>\nAbstract: We continue our initial study of Cp(X) spaces that are distinguished, equiv., are [&#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\/25357"}],"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=25357"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25357\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=25357"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=25357"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=25357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}