Cone space

Definition
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 defining ingredient::closed unit interval $$[0,1]$$ and we use the defining ingredient::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 $$[0,1]$$.

Refer:


 * Cone space functor to see the properties of the cone space functor
 * Cone-realizable space to see the property of a topological space being realizable as the cone space over some space