Definition:Loop (Topology)

This page is about Loop in the context of Topology. For other uses, see Loop.

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 $\map \gamma 0$.

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)

Also see

• Definition:Fundamental Group
• Definition:Closed Contour

Sources

• 2000: James R. Munkres: Topology (2nd ed.): $9$: The Fundamental Group: $\S 52$: The Fundamental Group