Suspension (topology)

In topology, the suspension SX of a topological space X is the quotient space:

of the product of X with the unit interval I = [0, 1]. Thus, X is stretched into a cylinder and then both ends are collapsed to points. One views X as "suspended" between the end points. One can also view the suspension as two cones on X glued together at their base (or as a quotient of a single cone).