Naïve set theory MOC

Constant map

A constant map 𝑐𝑇 :𝑋 →𝑌 is a map whose range 𝑐𝑇𝑋 consists of a single element 𝑐 ∗. general A map is constant iff it can be factored via the single point space, hence it always has the form 𝑐𝑇 where 𝑇 :𝑋 → ∗ is the unique morphism.

Properties

Topology

• A homotopy between constant maps is a continuous path. Therefore, a space is path-connected iff all constant maps form a single homotopy class.
• A map is null-homotopic iff it is homotopy to a constant map

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