Definition:Loop (Topology)/Topological Manifold

Definition

Let $M$ be a topological manifold.

Let $\sigma : \closedint 0 1 \to M$ be a continuous path.

Let $\map \sigma 0 = \map \sigma 1$.

Then $\sigma$ is called a loop.

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 6$: Geodesics and Distance. Completeness