Definition:Loop (Topology)
(Redirected from Definition:Closed Path (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
- 2000: James R. Munkres: Topology (2nd ed.): $9$: The Fundamental Group: $\S 52$: The Fundamental Group