Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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?

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.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.