Loop (topology)

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A loop in mathematics, in a topological space X is a path 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 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.

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