Definition:Loop (Topology)/Constant Loop
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Definition
Let $T$ be a topological space.
Let $p \in T$.
Let $\map \Omega {T, p}$ denote the set of all loops based at $p$.
A constant loop $c_p$ is the loop $c_p \in \map \Omega {T, p}$ such that:
- $\forall t \in \closedint 0 1 : \map {c_p} t = p$
Also see
Sources
- 2011: John M. Lee: Introduction to Topological Manifolds (2nd ed.) ... (previous) ... (next): $\S 7$: Homotopy and the Fundamental Group. Homotopy