In a locally contractible space can we find local bases of contractible sets whose closures are locally contractible? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T07:25:16Z http://mathoverflow.net/feeds/question/37380 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/37380/in-a-locally-contractible-space-can-we-find-local-bases-of-contractible-sets-whos In a locally contractible space can we find local bases of contractible sets whose closures are locally contractible? Spiros Adams-Florou 2010-09-01T14:17:46Z 2010-09-01T14:17:46Z <p>In a locally contractible topological space $X$ is it possible at each point $x$ to find a local basis of contractible sets $U_i\ni x$ such that the closure of each set $\overline{U_i} \subset X$ is also locally contractible? </p> <p>More precisely, for this question we may assume $X$ is compact and is an ANR (for the class of separable metric spaces), we can even assume that $X$ is embedded as a subspace of $\mathbb{R}^n$ if that makes the question easier.</p>