A loop in mathematics, in a topological space X is a path f from the unit interval I = to X such that f(0) = f(1). In other words, it is a path whose initial point is equal to the terminal point.
A loop may also be seen as a continuous map f from the unit circle S1 into X, because S1 may be regarded as a quotient of I under the identification 0 ∼ 1.
The set of all loops in X forms a space called the loop space of X.