Remark 3.6.2.4. Let $X$ and $Y$ be simplicial sets having at most countably many simplices of each dimension. Then the comparison map $\theta _{X,Y}: |X \times Y| \rightarrow |X| \times |Y|$ is a homeomorphism. For a proof, we refer the reader to [MR0084138].
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$