Definition 1

Let X be a topological space. A path in X is called any continuous mapping $c$ of $\mathbf{I}$ into X. The point $c(0)$ is called the origin, the point $c(1)$ the term of the path $c$. A loop in X is called a path in X whose origin is equal to the term.

Let $x$ and $y$ be points of X. One says that a path $c$ in X joins $x$ to $y$ if $x$ is its origin and $y$ is its term.