Loop (topology)

In mathematics, a loop in a topological spaceX is a continuous functionf from the unit intervalI = [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.

A loop may also be seen as a continuous map f from the pointedunit circleS into X, because S 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.