most recent 30 from http://mathoverflow.net 2013-05-24T05:57:54Z http://mathoverflow.net/feeds/question/28775 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/28775/when-can-boundedness-be-characterized-topologically-in-metric-spaces Garabed Gulbenkian 2010-06-19T19:30:56Z 2010-06-19T20:23:03Z

<p>Let H be a separable and infinite-dimensional Hilbert space. Is every closed subset of H homeomorphic to some closed and bounded subset of H?</p>

http://mathoverflow.net/questions/28775/when-can-boundedness-be-characterized-topologically-in-metric-spaces/28777#28777 Ady 2010-06-19T20:23:03Z 2010-06-19T20:23:03Z

<p>It is an old result of Klee saying that the infinite-dimensional Hilbert space is homeomorphic with both its unit sphere and its closed unit ball. See e.g. <a href="http://www.ams.org/journals/bull/1961-67-03/S0002-9904-1961-10589-2/S0002-9904-1961-10589-2.pdf" rel="nofollow">http://www.ams.org/journals/bull/1961-67-03/S0002-9904-1961-10589-2/S0002-9904-1961-10589-2.pdf</a> , and the references therein.</p>