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# Loop

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 known as the basepoint. Formally, if is a topological space and , a loop is a continuous map

such that and .

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.

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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## References

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

Loop

## Cite this as:

Renze, John; Stover, Christopher; and Weisstein, Eric W. "Loop." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Loop.html