I'm studying basic Algebraic Topology. Here is my question:
Let $X$ be a space with $\pi_i(X)=0$ for all $i$.
Then, $X$ should be contractible?
(If $X$ is CWcomplex, then cellby cell argument works and this is true.)
I'm studying basic Algebraic Topology. Here is my question: Let $X$ be a space with $\pi_i(X)=0$ for all $i$. Then, $X$ should be contractible? (If $X$ is CWcomplex, then cellby cell argument works and this is true.) 

closed as too localized by Mark Grant, Gjergji Zaimi, Ryan Budney, Loop Space, Andreas Thom Dec 7 '11 at 12:44This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 

