Suspension

Definition

Given a topological space $X$, the suspension of $X$, denoted $SX$, is defined as the quotient of $X\times I$ by the following two equivalence relations:

$(x_1,0)\simeq (x_2,0)$

and

$(x_1,1)\simeq (x_2,1)$

In other words, both ends of the cylinder are shrunk to a point.