Homotopy of continuous maps

Null-homotopic map

A morphism of topological spaces $𝑓 : 𝑋 \to 𝑌$ is said to be null-homotopic iff it is homotopic to a Constant map. #m/def/homotopy The same is said for loops under Homotopy of paths.

Properties

In a path-connected space null-homotopic maps form a single homotopy class denoted $0$ , since $0 \circ [𝑓] = [𝑓] \circ 0 = 0$ .
A space $𝑋$ is contractible iff the identity $i d 𝑋$ is null-homotopic.

#state/tidy | #lang/en | #SemBr