Definition:Loop (Topology)/Simple
< Definition:Loop (Topology)(Redirected from Definition:Simple Loop (Topology))
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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 simple loop (in $T$) if and only if:
- $\map \gamma {t_1} \ne \map \gamma {t_2}$ for all $t_1 ,t_2 \in \hointr 0 1$ with $t_1 \ne t_2$
- $\map \gamma 0 = \map \gamma 1$
Also see
Sources
- 2000: James R. Munkres: Topology (2nd ed.): $10$: Separation Theorems in the Plane: $\S 66$: The Cauchy Integral Formula