[[Topological retraction]]
# The boundary of a ball is not a retract

The subspace $\mathbb{S}^n \sube \mathbb{B}^{n+1}$ is not a retract for any $n \in \mathbb{N}$,
i.e. there exists no continuous map $r : \mathbb{B}^{n+1} \twoheadrightarrow \mathbb{S}^n$ with $r \iota = \id_{\mathbb{S}^n}$. #m/thm/topology 

> [!missing]- Proof
> #missing/proof

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