Closed copies of $\mathbb{N}$ in ${\mathbb{R}}^{{\omega }_1}$

We investigate closed copies of~$\mathbb{N}$ in powers of~$\mathbb{R}$ with respect to $C^{\ast }$- and $C$-embedding. We show that ${\mathbb{R}}^{{\omega }_1}$ contains closed copies of~$\mathbb{N}$ that are not $C^{\ast }$-embedded.