Definition:Concatenation of Paths

Definition
Let $X$ be a topological space.

Let $f,g: [0,1] \to X$ be paths.

Suppose that $f(1) = g(0)$.

The composition of $f$ and $g$ is the mapping $fg: [0,1] \to X$ defined by:


 * $\displaystyle fg(s)= \begin{cases}

f(2s) & 0 \le s \le \frac 1 2 \\ g(2s-1) & \frac 1 2 \le s \le 1 \end{cases}$

Also known as
The composition of paths is also called concatenation or product.

Also see

 * Composition of Paths is Path