In mathematics, a loop in a topological space is a continuous function from the unit interval to such that In other words, it is a path whose initial point is equal to its terminal point..
A loop may also be seen as a continuous map from the pointed unit circle into , because may be regarded as a quotient of under the identification of 0 with 1.
The set of all loops in forms a space called the loop space of .
Definition Let be a topological space. A loop is a continuous function such that . If begins and ends at the loop is said to be based at . A loop is then a path that begins and ends at the same point .
The set of homotopy classes of loops based at together with the operation of path composition, forms the fundamental group of relative to , usually denoted by .
See also Free loop Loop group Loop space Loop algebra Fundamental group Quasigroup
References
es:Grupo fundamental#Lazo