Loop (topology)

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In mathematics, a loop 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.

[edit] See also

• Free loop
• Loop group
• Loop space
• Loop algebra