{"id":26470,"date":"2023-01-01T10:46:19","date_gmt":"2023-01-01T09:46:19","guid":{"rendered":"https:\/\/cio.umh.es\/?p=26470"},"modified":"2022-12-12T10:50:58","modified_gmt":"2022-12-12T09:50:58","slug":"ferrando-j-c-gabriyelyan-s-2023-properties-of-the-weak-and-weak-%e2%88%97-topologies-of-function-spaces-revista-de-la-real-academia-de-ciencias-exactas-fisicas-y-naturales-serie","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2023\/01\/01\/ferrando-j-c-gabriyelyan-s-2023-properties-of-the-weak-and-weak-%e2%88%97-topologies-of-function-spaces-revista-de-la-real-academia-de-ciencias-exactas-fisicas-y-naturales-serie\/","title":{"rendered":"Ferrando, J.C., Gabriyelyan, S. (2023) &quot;Properties of the weak and weak \u2217 topologies of function spaces&quot;, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales &#8211; Serie A: Matematicas, 117 (1):20"},"content":{"rendered":"<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Juan Carlos Ferrando (Center of Operations Research, Miguel Hern\u00e1ndez University of Elche) and Saak Gabriyelyan (Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva)<\/strong><\/p>\n<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Abstract: <\/strong>Let X be a Tychonoff space, and let S be a directed family of functionally bounded subsets of X containing all finite subsets of X. Denote by CTS(X) the space of all continuous functions on X endowed with the topology of uniform convergence on the sets of the family S. We characterize X for which the space CTS(X) endowed with the weak topology satisfies numerous weak barrelledness conditions or (DF)-type properties, or it has a locally convex property stronger than the property of being a Mackey space. It is shown that the dual space of CTS(X) is weak<sup>\u2217<\/sup>sequentially Ascoli iff X is finite. We prove also that if CTS(X) is an \u2113<sub>\u221e<\/sub>-quasibarrelled space, then the strong dual of CTS(X) is a weakly sequentially Ascoli space iff X is finite.<\/p>","protected":false},"excerpt":{"rendered":"<p>Juan Carlos Ferrando (Center of Operations Research, Miguel Hern\u00e1ndez University of Elche) and Saak Gabriyelyan (Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva)<br \/>\nAbstract: Let X be a Tychonoff space, and let S be a directed family of functionally bounded subsets of X containing all finite subsets of X. Denote by CTS(X) the space of [&#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\/26470"}],"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=26470"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/26470\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=26470"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=26470"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=26470"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}