Let $X$ be a topological space. The suspension of $X$, denoted $ΣX$, is the quotient $CX / (X × ${$1$}$)$, where $CX$ is the cone on $X$, the quotient space $(X × [0, 1]) / (X × ${$0$}$)$.
Is $ΣX$ contractible. How can I prove this?
2026-03-26 14:19:55.1774534795
Is the suspension space contractible?
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A suspension is not in general contractible. To see this, note that the suspension of $S^n$ is $S^{n + 1}$, which is not contractible.