Definition:Homotopy Class/Path
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $f: \closedint 0 1 \to S$ be a path in $T$.
The homotopy class of the path $f$ is the homotopy class of $f$ relative to $\set {0, 1}$.
That is, the equivalence class of $f$ under the equivalence relation defined by path-homotopy.
Also see
Also known as
The homotopy class of $f$ is also sometimes called as the path class of $f$.
Sources
- 2011: John M. Lee: Introduction to Topological Manifolds (2nd ed.) ... (previous) ... (next): $\S 7$: Homotopy and the Fundamental Group. Homotopy
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- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 6$: Geodesics and Distance. Closed Geodesics