Definition:Concatenation of Paths

Definition
Let $X$ be a topological space.

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

Let $f(1)=g(0)$.

The composition of $f$ and $g$ is the function $fg:[0,1]\to X$ defined by:
 * $\displaystyle fg(s)=\begin{cases}f(2s) & 0\leq s\leq \frac12\\

g(2s-1) & \frac12 \leq s \leq 1 \end{cases}$

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

Also see

 * Composition of Paths is Path