most recent 30 from http://mathoverflow.net 2013-06-18T21:04:18Z http://mathoverflow.net/feeds/question/34384 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/34384/omplete-homogeneous-space-which-is-not-locally-compact Ivan Gundyrev 2010-08-03T13:36:23Z 2010-08-03T14:21:57Z

<p>It is well-known theorem that every locally compact, homogeneous, metric space is complete. Does anybody know example of complete, homogeneous, metric space which is not locally compact?</p>

http://mathoverflow.net/questions/34384/omplete-homogeneous-space-which-is-not-locally-compact/34386#34386 Anweshi 2010-08-03T13:56:36Z 2010-08-03T14:21:57Z

<p>A Banach space is homogeneous since the metric is arising from a norm. An infinite dimensional Banach space has the property that its unit ball is not compact; therefore the space is not locally compact.</p> <p>For a concrete example, take the space of continuous real functions on an interval with the supremum norm.</p>