In mathematics, a **loop** in a topological space X is a continuous function f from the unit interval *I* = [0,1] to X such that *f*(0) = *f*(1). In other words, it is a path whose initial point is equal to its terminal point.^{[1]}

A loop may also be seen as a continuous map f from the pointed unit circle *S*^{1} into X, because *S*^{1} may be regarded as a quotient of I under the identification of 0 with 1.

The set of all loops in X forms a space called the loop space of X.^{[1]}