{"id":3972,"date":"2017-10-25T08:40:07","date_gmt":"2017-10-25T08:40:07","guid":{"rendered":"http:\/\/cio.edu.umh.es\/?p=3972"},"modified":"2017-10-25T08:40:07","modified_gmt":"2017-10-25T08:40:07","slug":"conferencia-del-profesor-gerald-beer","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2017\/10\/25\/conferencia-del-profesor-gerald-beer\/","title":{"rendered":"Conferencia del Profesor Gerald Beer"},"content":{"rendered":"<p>[:es]<span style=\"color: #000000\"><strong>Title<\/strong>:\u00a0<span lang=\"EN-US\">Uniform continuity of the product of real functions defined on a metric space<\/span><\/span><br \/>\n<span style=\"color: #000000\"><strong>Speaker<\/strong>:\u00a0Gerald Beer (California State University Los Angeles)<\/span><br \/>\n<span style=\"color: #000000\"><strong>Date<\/strong>: 03\/11\/2017, 13:00h<\/span><br \/>\n<span style=\"color: #000000\"><strong>Location<\/strong>:\u00a0Sala de Seminarios (Edificio Torretamarit)<\/span><br \/>\n<span style=\"color: #000000\"><strong>Abstract:<\/strong><\/span><br \/>\n<span style=\"color: #000000\">As is well-known, the pointwise product of two bounded real-valued uniformly continuous functions f \u00a0and g\u00a0 defined on a metric space is uniformly continuous, but this condition is hardly necessary:\u00a0 let\u00a0\u00a0\u00a0\u00a0\u00a0 f(x) = g(x) = \\sqrt (x) for x \u2265 0.\u00a0 In joint work with Som Naimpally (deceased) that appeared in Real Analysis Exchange in 2012, we produce necessary and sufficient conditions on a pair of uniformly continuous real-valued functions (f,g) defined on an arbitrary\u00a0 metric space so that their pointwise product is uniformly continuous.\u00a0 Our conditions are sufficient for any pair of real-valued functions, and are necessary for a class of pairs properly containing the uniformly continuous pairs.\u00a0 We precisely identify this class and describe it in various ways.<\/span><br \/>\n<span style=\"color: #000000\">A different but equally interesting question is this:\u00a0 what are necessary and sufficient conditions on the internal structure of a metric space so that the product of each pair of uniformly continuous real-valued functions remains uniformly continuous?\u00a0\u00a0 In joint work with Maribel Garrido and Ana Mero\u00f1o appearing in Set-Valued and Variational Analysis and dedicated to Jon Borwein that in part revisits a recent result of Javier Cabello S\u00e1nchez appearing in Filomat, we show that this occurs exactly when the familiar bornology of Bourbaki bounded subsets coincides with a new larger bornology.<\/span>[:]<\/p>","protected":false},"excerpt":{"rendered":"<p>[:es]Title:\u00a0Uniform continuity of the product of real functions defined on a metric space<br \/>\nSpeaker:\u00a0Gerald Beer (California State University Los Angeles)<br \/>\nDate: 03\/11\/2017, 13:00h<br \/>\nLocation:\u00a0Sala de Seminarios (Edificio Torretamarit)<br \/>\nAbstract:<br \/>\nAs is well-known, the pointwise product of two bounded real-valued uniformly continuous functions f \u00a0and g\u00a0 defined on a metric space is uniformly continuous, but this condition is hardly necessary:\u00a0 let\u00a0\u00a0\u00a0\u00a0\u00a0 [&#8230;]<\/p>","protected":false},"author":3477,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/3972"}],"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\/3477"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=3972"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/3972\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=3972"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=3972"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=3972"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}