Definition:Loop (Topology)

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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 $T$) if and only if:

$\gamma \left({0}\right) = \gamma \left({1}\right)$


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.

Internationalization

Loop is translated:

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


Also see


Sources