Homotopy equivalence

A homotopy equivalence is an isomorphism in $𝗁 𝖳 𝗈 𝗉$ . 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 maps)