Definition:Loop (Topology)/Simple

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

• Definition:Jordan Curve

Sources

• 2000: James R. Munkres: Topology (2nd ed.): $10$: Separation Theorems in the Plane: $\S 66$: The Cauchy Integral Formula