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 $T$) :
 * $\map \gamma {t_1} \ne \map \gamma {t_2}$ 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