Suspension

In topology, this is how the suspension is defined. Given a topological space $X$, first form the product $[0,1] \times X$, then the cone of $X$ is the quotient: $$\Sigma X=[0,1] \times X / (\{0\} \times X \sqcup \{1\} \times X).$$

We use suspension to create new spaces:

More generally, $$\Sigma {\bf S}^n = {\bf S}^{n+1}.$$

Compare to the product and the cone.