Example 3.2.2.7. Let $X$ be a topological space and let $x \in X$ be a base point, which we identify with a vertex of the singular simplicial set $\operatorname{Sing}_{\bullet }(X)$. For every positive integer $n$, we can identify $\pi _{n}( \operatorname{Sing}_{\bullet }(X), x)$ with the set $\pi _{n}(X,x)$ of (pointed) homotopy classes of maps from the sphere $S^ n \simeq | \Delta ^ n / \operatorname{\partial \Delta }^ n |$ into $X$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$