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Let $X$ and $Y$ be topological spaces, where $X$ is contractible. Is the quotient space $X/Y$ contractible?

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    $\begingroup$ Maybe Y is supposed to be contractible? Then the answer is positive if you work with CW complexes. I suspect that it is still negative in general. $\endgroup$ – Moishe Kohan Jun 2 '14 at 3:10
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No. Consider $X=[0,1]$ and $Y=\{0,1\}$.

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