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.

## 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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## References

Owen, P. *Knots.* Philadelphia, PA: Courage, p. 35, 1993.## Referenced on Wolfram|Alpha

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

## Subject classifications