The term "loop" has a number of meanings in mathematics.

Most simply, a loop is a closed curve whose initial and final points coincide in a fixed point p known as the basepoint. Formally, if X is a topological space and p in X, a loop is a continuous map


such that L(0)=p and L(1)=p.

A knot or hitch which holds its form rigidly is also called a loop (Owen 1993).

Other definitions appearing in particular area of mathematics include the algebraic loop and graph loop.

See also

Algebraic Loop, Bol Loop, Closed Curve, Generalized Bol Loop, Graph Loop, Half-Bol Identity, Loop Space, Moufang Loop, Trivial Loop

Portions of this entry contributed by Christopher Stover

Portions of this entry contributed by John Renze

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Owen, P. Knots. Philadelphia, PA: Courage, p. 35, 1993.

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Cite this as:

Renze, John; Stover, Christopher; and Weisstein, Eric W. "Loop." From MathWorld--A Wolfram Web Resource.

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