Definition 25.3 (The cone over a space):

Let $X$ be a topological space. The cone $C(X)$ over $X$ is the quotient space

$$C(X) = (X\times [0, 1])/(X\times \{0\})$$

in We have an obvious inclusion map $i:X\longrightarrow C(X)$ given by $i(x) = [x, 1]$ where the square bracket refers to the image of $(x, 1) \in X\times [0,1]$ in the quotient $C(X)$.