Homotopy equivalence

A homotopy equivalence is an isomorphism in $𝗁 𝖳 𝗈 𝗉$ . #m/def/homotopy Topological spaces $𝑋$ and $𝑌$ are homotopy equivalent iff there exist $𝑓 \in 𝖳 𝗈 𝗉 (𝑋, 𝑌)$ and $𝑔 \in 𝖳 𝗈 𝗉 (𝑌, 𝑋)$ so that $𝑔 𝑓 ≃ i d 𝑋$ and $𝑓 𝑔 ≃ i d 𝑌$ (Homotopy of continuous maps)

warning

This definition suffers from the same problem discussed in Equivalence of categories. Namely, there may be non-homotopic proofs that a map is a homotopy equivalence under this definition. #to/fix

Properties

A Homotopy invariant is shared by homotopy equivalent spaces.

#state/develop | #lang/en | #SemBr