# 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 $T$) if and only if:

$\map \gamma 0 = \map \gamma 1$

### Base Point

The base point of $\gamma$ is $\gamma \left ({0}\right)$.

## Also known as

A loop is also referred to as a closed path.

Some sources refer to it as a cycle.

## Internationalization

Loop is translated:

 In French: lacet In Dutch: lus (literally: loop)