Is Level set of Regular functions in Alexandrov spaces again an Alex. space? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T10:30:37Z http://mathoverflow.net/feeds/question/16790 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/16790/is-level-set-of-regular-functions-in-alexandrov-spaces-again-an-alex-space Is Level set of Regular functions in Alexandrov spaces again an Alex. space? MG 2010-03-01T22:08:31Z 2010-03-02T00:20:47Z <p>Let $X^n$ be an Alexandrov space, and $f: X^n\to \mathbb R^k$ a regular map, does the level set necessary be an Alexandrov space?</p> <p>In my mind, the intrinsic metric on the level set is 'comparable' to the ambient metric, but is it necessary an Alexandrov space?</p> http://mathoverflow.net/questions/16790/is-level-set-of-regular-functions-in-alexandrov-spaces-again-an-alex-space/16810#16810 Answer by Anton Petrunin for Is Level set of Regular functions in Alexandrov spaces again an Alex. space? Anton Petrunin 2010-03-02T00:20:47Z 2010-03-02T00:20:47Z <p>The answer is "no" even for regular semiconcave function $f:X\to\mathbb R$</p> <p>If $f:X\to \mathbb R$ is convex then it is a long-standing open problem.</p>