Definition:Loop (Topology)/Null-Homotopic Loop
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $\gamma$ be a loop in $T$.
Suppose $\gamma$ is path-homotopic to a constant loop.
Then $\gamma$ is said to be null-homotopic.
Also see
Sources
- 2011: John M. Lee: Introduction to Topological Manifolds (2nd ed.) ... (previous) ... (next): $\S 7$: Homotopy and the Fundamental Group. Homotopy