Cone space

Definition

Given a topological space $X$, the cone space of $X$, denoted as $CX$, is defined as the quotient of $X\times I$ by the equivalence relation:

$(x_1,0)\sim (x_2,0)\mathrm{\forall }{x}_1,x_2\in X$

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