Loop (topology)

Loop (topology)

In mathematics, a loop in a topological space "X" is a path "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 the terminal point.

A loop may also be seen as a continuous map "f" from the unit circle "S"1 into "X", because "S"1 may be regarded as a quotient of "I" under the identification 0 ∼ 1.

The set of all loops in "X" forms a space called the loop space of "X".

ee also

*Free loop
*Loop group
*Loop space
*Loop algebra


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