Cone space

Given a topological space $X$, the cone space of $X$, denoted as $CX$, is defined as the quotient of $X \times I$ (where $I$ is the closed unit interval $[0,1]$ and we use the product topology) by the equivalence relation:
$(x_1,0) \sim (x_2,0) \forall x_1,x_2 \in X$
Here, $I$ refers to the closed unit interval $[0,1]$.