Definition:Closed Path (Topology)

Definition
Let $X$ be a topological space.

Let $I \subset \R$ be the unit interval $\left[{0 \,.\,.\, 1}\right]$.

Let $c : I \to X$ be a path in $X$.

Then $c$ is said to be closed iff $c \left({0}\right) = c \left({1}\right)$.