Definition:Loop (Topology)/Topological Manifold
< Definition:Loop (Topology)(Redirected from Definition:Loop in Topological Manifold)
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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