Homotopy of maps

Null-homotopic map

A morphism of topological spaces 𝑓 :𝑋 →𝑌 is said to be null-homotopic iff it is homotopic to a Constant map. 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 ∘[𝑓] =[𝑓] ∘0 =0.
• A space 𝑋 is contractible iff the identity id𝑋 is null-homotopic.

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