Embeddings of $3$--manifolds via open books

In this note, we discuss embeddings of $3$–manifolds via open books. First we show that every open book of every closed orientable $3$–manifold admits an open book embedding in any open book decompistion of $S^2\times S^3$ and $S^2 \widetilde{\times} S^3$withthepageadiskbundleover$S^2$ and monodromy the identity. We then use open book embeddings to reprove that every closed orientable $3$–manifold embeds in $S^5\mathrm{.}$