Loop in a space

A loop in a topological space $X$ is a path
$$\gamma:[0,1]\rightarrow X$$such that $\gamma(0)=\gamma(1)$.

Remarks

• The common endpoint $\gamma(0)=\gamma(1)$ is called the base point of the loop. If this point is $x_{0}$, we say that $\gamma$ is a loop based at $x_{0}$.