Definition:Loop (Topology)

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $\gamma: \left[{0 \,.\,.\, 1}\right] \to S$ be a path in $T$.

$\gamma$ is a loop (in $T$) :
 * $\gamma \left({0}\right) = \gamma \left({1}\right)$

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

Also see

 * Definition:Fundamental Group
 * Definition:Closed Complex Contour