Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 1.1.8.13. Let $0 \leq i \leq n$. Combining Example 1.1.8.9 with Proposition 1.1.8.11, we see that the inclusion map $\Lambda ^{n}_{i} \hookrightarrow \Delta ^{n}$ induces a homeomorphism from $| \Lambda ^{n}_{i} |$ to the subset of $| \Delta ^{n} |$ given by

\[ \{ (t_0, \ldots , t_ n) \in | \Delta ^{n} |: t_ j = 0 \text{ for some $j \neq i$} \} . \]