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