The boundary of a ball is not a retract

The subspace $𝕊 𝑛 \subseteq 𝔹 𝑛 + 1$ is not a retract for any $𝑛 \in ℕ$ , i.e. there exists no continuous map $𝑟 : 𝔹 𝑛 + 1 ↠ 𝕊 𝑛$ with $𝑟 𝜄 = i d 𝕊 𝑛$ . topology