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 Resource. https://mathworld.wolfram.com/Loop.html
Subject classifications
![L:[0,1]->X](http://mathworld.wolfram.com/images/equations/Loop/NumberedEquation1.svg)
