Loop (topology)
In mathematics, a loop in a topological space "X" is a continuous function "f" from the unit interval "I" = [0,1] to "X" such that "f"(0) = "f"(1). 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 "f" from the pointed unit circle "S" into "X", because "S" may be regarded as a quotient of "I" under the identification of 0 with 1. The set of all loops in "X" forms a space called the loop space of "X". Loop (topology