Definition:Loop (Topology)

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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 $\gamma \left ({0}\right)$.


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)


Also see


Sources