Definition:Loop (Topology)/Constant Loop

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

• Constant Loop is Loop

Sources

• 2011: John M. Lee: Introduction to Topological Manifolds (2nd ed.) ... (previous) ... (next): $\S 7$: Homotopy and the Fundamental Group. Homotopy