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
Explore with Wolfram|Alpha
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
![L:[0,1]->X](/images/equations/Loop/NumberedEquation1.svg)
