Cone

A (geometric) cone is a subset of a vector space that contains all of its (positive) multiples: $$A={\bf R}A=\{\alpha v: v \in A,\alpha \in {\bf R}^+ \}.$$

Every subspace is a cone.

In topology, this is how cone is defined. Given a topological space $X$, first form the product $[0,1] \times X$, then the cone of $X$ is $$CX=[0,1] \times X / \{1\} \times X$$

It can be seen as a geometric cone if $X$ is closed subset of ${\bf R}^n$ and $N \in {\bf R}^n -X$. Then $$CX=\{xN:x \in X \},$$ the union of segments from $n$ to a point in $X$.

Compare to the product and the suspension.