Homotopy theory MOC

Homotopy equivalence

A homotopy equivalence is an isomorphism in 𝗁𝖳𝗈𝗉. #m/def/homotopy Topological spaces 𝑋 and 𝑌 are homotopy equivalent iff there exist 𝑓 ∈𝖳𝗈𝗉(𝑋,𝑌) and 𝑔 ∈𝖳𝗈𝗉(𝑌,𝑋) so that 𝑔𝑓 ≃id𝑋 and 𝑓𝑔 ≃id𝑌 (Homotopy of continuous maps)

Properties

• A Homotopy invariant is shared by homotopy equivalent spaces.

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