Let $(X,\mathscr{T})$ be a topological space. A loop in $X$ is a continuous map $\gamma:[0,1]\to X$ having the property that $$\gamma(0)=\gamma(1)$$

If $x=\gamma(0)=\gamma(1)$, then $x$ is the base point for the loop $\gamma$.

The trivial loop at $x$ is the loop $\gamma_{x}:t\mapsto x$.