Closed copies of $\mathbb{N}$ in ${\mathbb{R}}^{\ddot{I}{‰}_1}$

Abstract

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

Version 2: some corrections and reformulations Version 3: references to older results plus an example of a nonC*-embedded copy consistent with not-CH