Definition:Loop (Topology)/Base Point

Definition

Let $X$ be a topological space.

Let $\gamma: \closedint 0 1 \to X$ be a loop.

The base point of $\gamma$ is $\map \gamma 0$.

In other words, $\gamma$ is said to be based at $\map \gamma 0$.

Sources

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