Loop (in topology)

A closed path. In detail, a loop $f$ is a continuous mapping of the interval $[0,1]$ into a topological space $X$ such that $f(0) = f(1)$. The set of all loops in a space $X$ with a distinguished point $\star$ for which $f(0) = f(1) = {\star}$ forms the loop space $\Omega X$.