{"id":25363,"date":"2021-10-14T13:09:05","date_gmt":"2021-10-14T11:09:05","guid":{"rendered":"https:\/\/cio.umh.es\/?p=25363"},"modified":"2022-01-14T13:10:15","modified_gmt":"2022-01-14T12:10:15","slug":"ferrando-j-c-lopez-alfonso-s-2021-on-weakly-compact-sets-in-cx-revista-de-la-real-academia-de-ciencias-exactas-fisicas-y-naturales-serie-a-matematicas-115-238-2","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2021\/10\/14\/ferrando-j-c-lopez-alfonso-s-2021-on-weakly-compact-sets-in-cx-revista-de-la-real-academia-de-ciencias-exactas-fisicas-y-naturales-serie-a-matematicas-115-238-2\/","title":{"rendered":"Ferrando, J.C., L\u00f3pez-Alfonso, S. (2021) \u00abOn weakly compact sets in C(X)\u00bb, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales &#8211; Serie A: Matematicas, 115 (2):38"},"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 Salvador L\u00f3pez-Alfonso\u00a0 (Depto. Construcciones Arquitect\u00f3nicas, Universitat Polit\u00e8cnica de Val\u00e8ncia)<\/strong><\/p>\n<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Abstract: <\/strong>A subset A of a locally convex space E is called (relatively) sequentially complete if every Cauchy sequence {xn}n=1\u221e in E contained in A converges to a point x\u2208 A (a point x\u2208 E). Asanov and Velichko proved that if X is countably compact, every functionally bounded set in C<sub>p<\/sub>(X) is relatively compact, and Baturov showed that if X is a Lindel\u00f6f \u03a3 -space, each countably compact (so functionally bounded) set in C<sub>p<\/sub>(X) is a monolithic compact. We show that if X is a Lindel\u00f6f \u03a3 -space, every functionally bounded (relatively) sequentially complete set in C<sub>p<\/sub>(X) or in C<sub>w<\/sub>(X) , i.\u00a0e., in C<sub>k<\/sub>(X) equipped with the weak topology, is (relatively) Gul\u2019ko compact. We get some consequences.<\/p>","protected":false},"excerpt":{"rendered":"<p>Juan Carlos Ferrando (Operations Research Center, University Miguel Hern\u00e1ndez of Elche) and Salvador L\u00f3pez-Alfonso\u00a0 (Depto. Construcciones Arquitect\u00f3nicas, Universitat Polit\u00e8cnica de Val\u00e8ncia)<br \/>\nAbstract: A subset A of a locally convex space E is called (relatively) sequentially complete if every Cauchy sequence {xn}n=1\u221e in E contained in A converges to a point x\u2208 A (a point x\u2208 E). [&#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\/25363"}],"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=25363"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/25363\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=25363"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=25363"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=25363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}