most recent 30 from http://mathoverflow.net 2013-06-18T07:19:57Z http://mathoverflow.net/feeds/user/24700 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/100612/contractible-open-sets/100629#100629 Juan Ahtziri 2012-06-25T20:11:28Z 2012-06-26T09:18:35Z

<p>@Mariano: In my situation the function is not a Morse function and the curves of level are connected by paths, I think that this hypothesis about U are enough, but I can't proof this affirmation.</p> <p>@Anton: I don't know if the Whitehead manifold has a function with this properties.</p> <p>I want to proof that the compact sets $K_m = U-f^{-1}([0,m])$ (assuming that $0$ is the minimum value of $f$) are simply-connected, this will implies that $U$ is simply-connected to infinite.</p>