{"id":26233,"date":"2022-09-26T13:03:57","date_gmt":"2022-09-26T11:03:57","guid":{"rendered":"https:\/\/cio.umh.es\/?p=26233"},"modified":"2022-09-26T13:03:57","modified_gmt":"2022-09-26T11:03:57","slug":"ferrando-j-c-2022-approximation-by-pointwise-bounded-sets-of-continuous-functions-topology-and-its-applications-317108191","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2022\/09\/26\/ferrando-j-c-2022-approximation-by-pointwise-bounded-sets-of-continuous-functions-topology-and-its-applications-317108191\/","title":{"rendered":"Ferrando, J.C. (2022) \u00abApproximation by pointwise bounded sets of continuous functions\u00bb, Topology and its Applications, 317:108191"},"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)\u00a0<\/strong><\/p>\n<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Abstract: <\/strong>Assuming that X is a Tychonoff space, we obtain necessary and sufficient conditions for a function f\u2208R<sup>X<\/sup>to belong to the closure in R<sup>X<\/sup>of a pointwise bounded family F in C(X), the ring of real-valued continuous functions on X. In other words, if M(X) stands for the bidual of the space C<sub>p<\/sub>(X), equipped with the pointwise topology, we provide necessary and sufficient conditions for a function f\u2208R<sup>X<\/sup>to belong to M(X). As a noteworthy fact, if M, S and R are, respectively, the Michael, the Sorgenfrey, and the real line, it is shown that C(M)\u2288M(R) but C(S)\u2286M(R).<\/p>","protected":false},"excerpt":{"rendered":"<p>Juan Carlos Ferrando (Operations Research Center, University Miguel Hern\u00e1ndez of Elche)\u00a0<br \/>\nAbstract: Assuming that X is a Tychonoff space, we obtain necessary and sufficient conditions for a function f\u2208RXto belong to the closure in RXof a pointwise bounded family F in C(X), the ring of real-valued continuous functions on X. In other words, if M(X) stands [&#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\/26233"}],"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=26233"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/26233\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=26233"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=26233"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=26233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}