Definition:Loop (Topology)

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $\gamma: \closedint 0 1 \to S$ be a path in $T$.

$\gamma$ is a loop (in $T$) :
 * $\map \gamma 0 = \map \gamma 1$

Also known as
A loop is also referred to as a closed path.

Some sources refer to it as a cycle.

Also see

 * Definition:Fundamental Group
 * Definition:Closed Contour